WorldCat Identities

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
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Most widely held works about Nolan R Wallach
 
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
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 finite-dimensional 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

Real reductive groups by Nolan R Wallach( Book )

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). Self-contained 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 one-year 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 highly-acclaimed 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) - Self-contained 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 one-year 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

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 August-September 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
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

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
Representation theory and complex analysis : lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 10-17, 2004 by M Cowling( )

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
Real reductive groups by Nolan R Wallach( Book )

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

Real reductive groups by Nolan R Wallach( Book )

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

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

Harmonic analysis, group representations, automorphic forms, and invariant theory : in honor of Roger E. Howe by Jian-Shu 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, 9-11 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
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 self-contained 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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Audience level: 0.64 (from 0.03 for Harmonic a ... to 0.95 for Lie groups ...)

WorldCat IdentitiesRelated Identities
Representations and invariants of the classical groups
Alternative Names
Nolan Wallach Mathematician

Wallach, N.

Wallach, N. 1940-

Wallach, N. R. 1940-

Wallach, Nolan

Wallach, Nolan 1940-

Languages
English (187)

Italian (1)

Covers
Representations and invariants of the classical groupsReal reductive groupsSymmetry, representations, and invariantsReal reductive groupsRepresentation theory and complex analysis : lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 10-17, 2004Real reductive groupsReal reductive groupsReal Reductive Groups I