Wallach, Nolan R.
Overview
Works:  42 works in 215 publications in 2 languages and 4,257 library holdings 

Genres:  Conference papers and proceedings Filmed speeches Juvenile works 
Roles:  Author, Editor, Honoree, Dedicatee, Other, Contributor 
Classifications:  QA387, 512.55 
Publication Timeline
.
Most widely held works about
Nolan R Wallach
 Symmetry : representation theory and its applications : in honor of Nolan R. Wallach by Roger Howe( Book )
Most widely held works by
Nolan R Wallach
Continuous cohomology, discrete subgroups, and representations of reductive groups by
Armand Borel(
Book
)
30 editions published between 1980 and 2014 in English and held by 753 WorldCat member libraries worldwide
It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades
30 editions published between 1980 and 2014 in English and held by 753 WorldCat member libraries worldwide
It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades
Representations and invariants of the classical groups by
Roe Goodman(
Book
)
16 editions published between 1998 and 2003 in English and held by 478 WorldCat member libraries worldwide
As a text for those new to the area, this book provides an introduction to the structure and finitedimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. It makes abundant use of examples and more than 300 exercises (most with hints for solution) to explain concepts such as root systems, Weyl groups, and highest weight theory. For the more advanced reader, the book presents an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. It also serves as a reference for the main results concerning tensor and polynomial invariants and the finite dimensional representation theory of the classical groups
16 editions published between 1998 and 2003 in English and held by 478 WorldCat member libraries worldwide
As a text for those new to the area, this book provides an introduction to the structure and finitedimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. It makes abundant use of examples and more than 300 exercises (most with hints for solution) to explain concepts such as root systems, Weyl groups, and highest weight theory. For the more advanced reader, the book presents an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. It also serves as a reference for the main results concerning tensor and polynomial invariants and the finite dimensional representation theory of the classical groups
Harmonic analysis on homogeneous spaces by
Nolan R Wallach(
Book
)
16 editions published between 1973 and 1990 in English and Undetermined and held by 423 WorldCat member libraries worldwide
16 editions published between 1973 and 1990 in English and Undetermined and held by 423 WorldCat member libraries worldwide
Real reductive groups by
Nolan R Wallach(
Book
)
in English and held by 312 WorldCat member libraries worldwide
in English and held by 312 WorldCat member libraries worldwide
Symmetry, representations, and invariants by
Roe Goodman(
Book
)
26 editions published in 2009 in English and held by 293 WorldCat member libraries worldwide
"Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus. Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux). Selfcontained chapters, appendices, comprehensive bibliography More than 350 exercises (most with detailed hints for solutions) further explore main concepts. Serves as an excellent main text for a oneyear course in Lie group theory Benefits physicists as well as mathematicians as a reference work. Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highlyacclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants:  Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus  Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux)  Selfcontained chapters, appendices, comprehensive bibliography  More than 350 exercises (most with detailed hints for solutions) further explore main concepts  Serves as an excellent main text for a oneyear course in Lie group theory  Benefits physicists as well as mathematicians as a reference work."Publisher's website
26 editions published in 2009 in English and held by 293 WorldCat member libraries worldwide
"Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus. Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux). Selfcontained chapters, appendices, comprehensive bibliography More than 350 exercises (most with detailed hints for solutions) further explore main concepts. Serves as an excellent main text for a oneyear course in Lie group theory Benefits physicists as well as mathematicians as a reference work. Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highlyacclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants:  Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus  Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux)  Selfcontained chapters, appendices, comprehensive bibliography  More than 350 exercises (most with detailed hints for solutions) further explore main concepts  Serves as an excellent main text for a oneyear course in Lie group theory  Benefits physicists as well as mathematicians as a reference work."Publisher's website
Symplectic geometry and Fourier analysis by
Nolan R Wallach(
Book
)
12 editions published between 1976 and 1977 in English and held by 263 WorldCat member libraries worldwide
12 editions published between 1976 and 1977 in English and held by 263 WorldCat member libraries worldwide
New developments in Lie theory and their applications by
Juan Tirao(
Book
)
14 editions published in 1992 in English and held by 252 WorldCat member libraries worldwide
Representation theory, and more generally Lie theory, has played a very important role in many of the recent developments of mathematics and in the interaction of mathematics with physics. In AugustSeptember 1989, a workshop (Third Workshop on Representation Theory of Lie Groups and its Applications) was held in the environs of C6rdoba, Argentina to present expositions of important recent developments in the field that would be accessible to graduate students and researchers in related fields. This volume contains articles that are edited versions of the lectures (and short courses) given at the workshop. Within representation theory, one of the main open problems is to determine the unitary dual of a real reductive group. Although this prob lem is as yet unsolved, the recent work of Barbasch, Vogan, Arthur as well as others has shed new light on the structure of the problem. The article of D. Vogan presents an exposition of some aspects of this prob lem, emphasizing an extension of the orbit method of Kostant, Kirillov. Several examples are given that explain why the orbit method should be extended and how this extension should be implemented
14 editions published in 1992 in English and held by 252 WorldCat member libraries worldwide
Representation theory, and more generally Lie theory, has played a very important role in many of the recent developments of mathematics and in the interaction of mathematics with physics. In AugustSeptember 1989, a workshop (Third Workshop on Representation Theory of Lie Groups and its Applications) was held in the environs of C6rdoba, Argentina to present expositions of important recent developments in the field that would be accessible to graduate students and researchers in related fields. This volume contains articles that are edited versions of the lectures (and short courses) given at the workshop. Within representation theory, one of the main open problems is to determine the unitary dual of a real reductive group. Although this prob lem is as yet unsolved, the recent work of Barbasch, Vogan, Arthur as well as others has shed new light on the structure of the problem. The article of D. Vogan presents an exposition of some aspects of this prob lem, emphasizing an extension of the orbit method of Kostant, Kirillov. Several examples are given that explain why the orbit method should be extended and how this extension should be implemented
Real reductive groups by
Nolan R Wallach(
Book
)
33 editions published between 1986 and 2005 in English and Undetermined and held by 131 WorldCat member libraries worldwide
Sequel to andquot;Real Reductive Groups Iandquot;, this book emphasizes more analytical aspects of representation theory, but retains its focus on the interaction between algebra, analysis and geometry, like the first volume. The two volumes comprise a complete introduction to representation theory
33 editions published between 1986 and 2005 in English and Undetermined and held by 131 WorldCat member libraries worldwide
Sequel to andquot;Real Reductive Groups Iandquot;, this book emphasizes more analytical aspects of representation theory, but retains its focus on the interaction between algebra, analysis and geometry, like the first volume. The two volumes comprise a complete introduction to representation theory
Representation theory and automorphic forms by
Paul J Sally(
Book
)
11 editions published in 1993 in English and Italian and held by 65 WorldCat member libraries worldwide
11 editions published in 1993 in English and Italian and held by 65 WorldCat member libraries worldwide
Some applications of group representations by
Nolan R Wallach(
Visual
)
6 editions published between 1990 and 2012 in English and held by 22 WorldCat member libraries worldwide
Presents examples of applications of Lie theory showing how the subject has gone beyond its roots. Where Lie initially envisioned the theory as a way of solving differential equations by reducing the number of variables, today it is often used to set certain problems in a larger context by increasing the number of variables. Although becoming larger, the problem can become simpler because of the power of abstraction in representation theory and because of the exploitation of symmetries in the new, larger system
6 editions published between 1990 and 2012 in English and held by 22 WorldCat member libraries worldwide
Presents examples of applications of Lie theory showing how the subject has gone beyond its roots. Where Lie initially envisioned the theory as a way of solving differential equations by reducing the number of variables, today it is often used to set certain problems in a larger context by increasing the number of variables. Although becoming larger, the problem can become simpler because of the power of abstraction in representation theory and because of the exploitation of symmetries in the new, larger system
Representation theory and complex analysis : lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 1017,
2004 by
M Cowling(
)
5 editions published in 2008 in English and held by 14 WorldCat member libraries worldwide
5 editions published in 2008 in English and held by 14 WorldCat member libraries worldwide
Symmetry : representation theory and its applications : in honor of Nolan R. Wallach by
Roger Howe(
Book
)
4 editions published in 2014 in English and held by 13 WorldCat member libraries worldwide
Symmetry has served as an organizing principle in Nolan R. Wallach's fundamental contributions to representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. This volume is a collection of 19 invited articles that pay tribute to the breadth and depth of Wallach's work. The mostly expository articles are written by distinguished mathematicians and contain sufficient preliminary material so as to reach the widest possible audience. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: {OCLCbr#A0} D. Barbasch K. Baur M. Bhargava B. Casselman D. Ciubotaru M. Colarusso T. J. Enright S. Evens W. T. Gan A. M. Garsia R. Gomez G. Gour B. H. Gross G. Han P. E. Harris J. Hong R. E. Howe {OCLCbr#A0} {OCLCbr#A0} M. Hunziker B. Kostant H. Kraft R. J. Miatello L. Ni W. A. Pruett G. W. Schwarz A. Touzé D. A. Vogan N. R. Wallach J. F. Willenbring F. L. Williams J. A. Wolf G. Xin O. Yacobi M. Zabrocki
4 editions published in 2014 in English and held by 13 WorldCat member libraries worldwide
Symmetry has served as an organizing principle in Nolan R. Wallach's fundamental contributions to representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. This volume is a collection of 19 invited articles that pay tribute to the breadth and depth of Wallach's work. The mostly expository articles are written by distinguished mathematicians and contain sufficient preliminary material so as to reach the widest possible audience. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: {OCLCbr#A0} D. Barbasch K. Baur M. Bhargava B. Casselman D. Ciubotaru M. Colarusso T. J. Enright S. Evens W. T. Gan A. M. Garsia R. Gomez G. Gour B. H. Gross G. Han P. E. Harris J. Hong R. E. Howe {OCLCbr#A0} {OCLCbr#A0} M. Hunziker B. Kostant H. Kraft R. J. Miatello L. Ni W. A. Pruett G. W. Schwarz A. Touzé D. A. Vogan N. R. Wallach J. F. Willenbring F. L. Williams J. A. Wolf G. Xin O. Yacobi M. Zabrocki
Real reductive groups by
Nolan R Wallach(
Book
)
2 editions published in 1988 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 8 WorldCat member libraries worldwide
Real reductive groups by
Nolan R Wallach(
Book
)
3 editions published in 1992 in English and held by 7 WorldCat member libraries worldwide
3 editions published in 1992 in English and held by 7 WorldCat member libraries worldwide
Real reductive groups by
Nolan R Wallach(
Book
)
in English and held by 6 WorldCat member libraries worldwide
in English and held by 6 WorldCat member libraries worldwide
Development in mathematics in the 19th century(
Book
)
1 edition published in 1979 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1979 in English and held by 4 WorldCat member libraries worldwide
Lie groups : history, frontiers and applications by
Nolan R Wallach(
Book
)
3 editions published in 1977 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1977 in English and held by 2 WorldCat member libraries worldwide
Harmonic analysis, group representations, automorphic forms, and invariant theory : in honor of Roger E. Howe by
JianShu Li(
)
3 editions published in 2007 in English and held by 0 WorldCat member libraries worldwide
This volume carries the same title as that of an international conference held at the National University of Singapore, 911 January 2006 on the occasion of Roger E. Howe's 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe's mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. Sample Chapter
3 editions published in 2007 in English and held by 0 WorldCat member libraries worldwide
This volume carries the same title as that of an international conference held at the National University of Singapore, 911 January 2006 on the occasion of Roger E. Howe's 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe's mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. Sample Chapter
Real Reductive Groups I by
Nolan R Wallach(
)
1 edition published in 1988 in English and held by 0 WorldCat member libraries worldwide
Real Productive Groups I
1 edition published in 1988 in English and held by 0 WorldCat member libraries worldwide
Real Productive Groups I
State spaces of operator algebras : basic theory, orientations and C*products by
Erik M Alfsen(
)
2 editions published in 2001 in English and held by 0 WorldCat member libraries worldwide
This selfcontained work, focusing on the theory of state spaces of C*algebras and von Neumann algebras, explains how the oriented state space geometrically determines the algebra. The theory of orientation of C*algebra state spaces is presented with a new approach that does not depend on Jordan algebras, and the theory of orientation of normal state spaces of von Neumann algebras is presented with complete proofs for the first time. The theory of operator algebras was initially motivated by applications to physics, but has recently found unexpected new applications to fields of pure mathematics as diverse as foliations and knot theory. Key features include: * first and only work devoted to state spaces of operator algebras contains much material not available in existing books * prerequisites are standard graduate courses in real and complex variables, measure theory, and functional analysis * complete proofs of basic results on operator algebras presented so that no previous knowledge in the field is needed * detailed introduction develops basic tools used throughout the text * numerous chapter remarks on advanced topics of independent interest with references to the literature, or discussion of applications to physics "State Spaces of Operator Algebras" is intended for specialists in operator algebras, as well as graduate students and mathematicians seeking an overview of the field. The introduction to C*algebras and von Neumann algebras may also be of interest in it own right for those wanting a quick introduction to basic concepts in those fields
2 editions published in 2001 in English and held by 0 WorldCat member libraries worldwide
This selfcontained work, focusing on the theory of state spaces of C*algebras and von Neumann algebras, explains how the oriented state space geometrically determines the algebra. The theory of orientation of C*algebra state spaces is presented with a new approach that does not depend on Jordan algebras, and the theory of orientation of normal state spaces of von Neumann algebras is presented with complete proofs for the first time. The theory of operator algebras was initially motivated by applications to physics, but has recently found unexpected new applications to fields of pure mathematics as diverse as foliations and knot theory. Key features include: * first and only work devoted to state spaces of operator algebras contains much material not available in existing books * prerequisites are standard graduate courses in real and complex variables, measure theory, and functional analysis * complete proofs of basic results on operator algebras presented so that no previous knowledge in the field is needed * detailed introduction develops basic tools used throughout the text * numerous chapter remarks on advanced topics of independent interest with references to the literature, or discussion of applications to physics "State Spaces of Operator Algebras" is intended for specialists in operator algebras, as well as graduate students and mathematicians seeking an overview of the field. The introduction to C*algebras and von Neumann algebras may also be of interest in it own right for those wanting a quick introduction to basic concepts in those fields
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Related Identities
 Goodman, Roe Author
 Borel, Armand Author
 Tirao, Juan 1942 Author Editor
 Howe, Roger Contributor Author Editor
 Hunziker, Markus Contributor Editor
 Willenbring, Jeb F. Contributor Editor
 Sally, Paul J. Jr 19332013 Other Author Editor
 Li, JianShu Author Editor
 Tan, EngChye Editor
 Zhu, ChenBo
Useful Links
Associated Subjects
Algebra Automorphic forms Combinatorial analysis Differential equations Differential equations, Partial Fourier analysis Geometry, Algebraic Group theory Harmonic analysis Homogeneous spaces Homology theory Invariants Lie, Sophus, Lie groups Linear algebraic groups Mathematical physics Mathematics Number theory Operator algebras Operator theory Quantum computing Quantum theory Representations of groups Statespace methods Symmetry (Mathematics) Symplectic manifolds Topological groups Vector bundles