Lusztig, George 1946
Overview
Works:  30 works in 131 publications in 3 languages and 2,707 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree 
Classifications:  QA171, 512.2 
Publication Timeline
.
Most widely held works by
George Lusztig
Introduction to quantum groups by
George Lusztig(
Book
)
36 editions published between 1993 and 2011 in English and held by 500 WorldCat member libraries worldwide
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specialized at roots of 1 and yield new objects, which include quantum versions of the semisimple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical bases having rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the KacMoody Lie algebras. Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook. **************************************** There is no doubt that this volume is a very remarkable piece of work ... Its appearance represents a landmark in the mathematical literature. Bulletin of the London Mathematical Society This book is an important contribution to the field and can be recommended especially to mathematicians working in the field. EMS Newsletter The present book gives a very efficient presentation of an important part of quantum group theory. It is a valuable contribution to the literature. Mededelingen van het Wiskundig Lusztig's book is very well written and seems to be flawless ... Obviously, this will be the standard reference book for the material presented and anyone interested in the DrinfeldJimbo algebras will have to study it very carefully. ZAA [T]his book is much more than an 'introduction to quantum groups.' It contains a wealth of material. In addition to the many important results (of which several are newat least in the generality presented here), there are plenty of useful calculations (commutator formulas, generalized quantum Serre relations, etc.). Zentralblatt MATH
36 editions published between 1993 and 2011 in English and held by 500 WorldCat member libraries worldwide
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specialized at roots of 1 and yield new objects, which include quantum versions of the semisimple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical bases having rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the KacMoody Lie algebras. Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook. **************************************** There is no doubt that this volume is a very remarkable piece of work ... Its appearance represents a landmark in the mathematical literature. Bulletin of the London Mathematical Society This book is an important contribution to the field and can be recommended especially to mathematicians working in the field. EMS Newsletter The present book gives a very efficient presentation of an important part of quantum group theory. It is a valuable contribution to the literature. Mededelingen van het Wiskundig Lusztig's book is very well written and seems to be flawless ... Obviously, this will be the standard reference book for the material presented and anyone interested in the DrinfeldJimbo algebras will have to study it very carefully. ZAA [T]his book is much more than an 'introduction to quantum groups.' It contains a wealth of material. In addition to the many important results (of which several are newat least in the generality presented here), there are plenty of useful calculations (commutator formulas, generalized quantum Serre relations, etc.). Zentralblatt MATH
The discrete series of GLn over a finite field by
George Lusztig(
Book
)
14 editions published in 1974 in English and held by 462 WorldCat member libraries worldwide
14 editions published in 1974 in English and held by 462 WorldCat member libraries worldwide
Characters of reductive groups over a finite field by
George Lusztig(
Book
)
15 editions published between 1984 and 2016 in English and Undetermined and held by 433 WorldCat member libraries worldwide
This book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups
15 editions published between 1984 and 2016 in English and Undetermined and held by 433 WorldCat member libraries worldwide
This book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups
Representations of finite Chevalley groups by
George Lusztig(
Book
)
19 editions published between 1978 and 1990 in English and held by 308 WorldCat member libraries worldwide
19 editions published between 1978 and 1990 in English and held by 308 WorldCat member libraries worldwide
Hecke algebras with unequal parameters by
George Lusztig(
Book
)
8 editions published in 2003 in English and held by 186 WorldCat member libraries worldwide
Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over padic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KLbasis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KLbasis also possess very interestin
8 editions published in 2003 in English and held by 186 WorldCat member libraries worldwide
Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over padic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KLbasis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KLbasis also possess very interestin
IwahoriHecke algebras and their representation theory : lectures given at the C.I.M.E. summer school held in Martina Franca,
Italy, June 28July 6, 1999 by
Ivan Cherednik(
Book
)
2 editions published in 2002 in English and held by 17 WorldCat member libraries worldwide
Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of IwahoriHecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on IwahoriHecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy
2 editions published in 2002 in English and held by 17 WorldCat member libraries worldwide
Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of IwahoriHecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on IwahoriHecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy
Intersection cohomology methods in representation theory by
George Lusztig(
Visual
)
4 editions published in 1990 in English and held by 11 WorldCat member libraries worldwide
4 editions published in 1990 in English and held by 11 WorldCat member libraries worldwide
Current developments in mathematics, 2002(
Book
)
1 edition published in 2003 in English and held by 10 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 10 WorldCat member libraries worldwide
Représentations unipotentes génériques et blocs des groupes réductifs finis by
Michel Broué(
Book
)
4 editions published in 1993 in German and French and held by 6 WorldCat member libraries worldwide
4 editions published in 1993 in German and French and held by 6 WorldCat member libraries worldwide
Reductive group actions with onedimensional quotient by
Hanspeter Kraft(
Book
)
1 edition published in 1992 in French and held by 5 WorldCat member libraries worldwide
1 edition published in 1992 in French and held by 5 WorldCat member libraries worldwide
Modular representations of finite groups of Lie type by
Roger W Carter(
Book
)
1 edition published in 1973 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1973 in English and held by 5 WorldCat member libraries worldwide
On the Green polynomials of classical groups by
George Lusztig(
Book
)
1 edition published in 1975 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 3 WorldCat member libraries worldwide
Special issue celebrating the 60th birthday of George Lusztig by
Akihiko Gyoja(
Book
)
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
Analyse et topologie sur les espaces singuliers : CIRM, 610 juillet 1981 by Colloque Analyse et topologie sur les espaces singuliers(
Book
)
2 editions published between 1982 and 1983 in French and held by 2 WorldCat member libraries worldwide
2 editions published between 1982 and 1983 in French and held by 2 WorldCat member libraries worldwide
Coxeter orbits and eigenspaces of Forbenius by
George Lusztig(
Book
)
1 edition published in 1976 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1976 in English and held by 2 WorldCat member libraries worldwide
Discrete Series of GLn Over a Finite Field. (AM81) by
George Lusztig(
Book
)
3 editions published between 1974 and 2016 in English and held by 1 WorldCat member library worldwide
3 editions published between 1974 and 2016 in English and held by 1 WorldCat member library worldwide
Characters of Reductive Groups over a Finite Field. (AM107) by
George Lusztig(
Book
)
3 editions published between 1984 and 2016 in English and held by 1 WorldCat member library worldwide
This book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups
3 editions published between 1984 and 2016 in English and held by 1 WorldCat member library worldwide
This book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups
Characters of Reductive Groups over a Finite Field. (AM107) by
George Lusztig(
)
1 edition published in 1984 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 0 WorldCat member libraries worldwide
Discrete Series of GLn Over a Finite Field. (AM81) by
George Lusztig(
)
1 edition published in 1975 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 0 WorldCat member libraries worldwide
Representation theory of Lie groups : proceedings of the SRC/LMS Research Symposium on Representations of Lie Groups, Oxford,
28 June15 July 1977 by
Michael Francis Atiyah(
)
2 editions published in 1980 in English and held by 0 WorldCat member libraries worldwide
3. The Poincare series of the loop space of a compact group4. The Weyl character formula; References; 5. Algebraic structure of Lie groups; I. Lie Groups and Lie Algebras; 1. Vector fields; 2. The Lie algebra of a Lie group; 3. The exponential map; 4. The adjoint representation; 5. Subgroups and subalgebras; 6. Quotients; 7. Homomorphisms and local homomorphisms; 8. The universal covering group; II. Semisimple Lie Algebras; 1. Generalities on Lie algebras; 2. Cartan subalgebras; 3. Roots; 4. Geometry of the root system; 5. Classification; 6. Real forms
2 editions published in 1980 in English and held by 0 WorldCat member libraries worldwide
3. The Poincare series of the loop space of a compact group4. The Weyl character formula; References; 5. Algebraic structure of Lie groups; I. Lie Groups and Lie Algebras; 1. Vector fields; 2. The Lie algebra of a Lie group; 3. The exponential map; 4. The adjoint representation; 5. Subgroups and subalgebras; 6. Quotients; 7. Homomorphisms and local homomorphisms; 8. The universal covering group; II. Semisimple Lie Algebras; 1. Generalities on Lie algebras; 2. Cartan subalgebras; 3. Roots; 4. Geometry of the root system; 5. Classification; 6. Real forms
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Algebra Algebraic fields Algebraic topology Approximation theory AstronomyAwards Award presentations Awards Bernstein polynomials Blocks (Group theory) Characters of groups Chevalley groups ChinaHong Kong Decomposition (Mathematics) Eigenvectors Fiber bundles (Mathematics) Finite fields (Algebra) Finite groups Fixed point theory Geometry, Algebraic Group schemes (Mathematics) Group theory Hecke algebras Hodge theory Homology theory Ktheory Lie groups Linear algebraic groups Mathematical physics Mathematics MathematicsAwards MedicineAwards Moduli theory Operator theory Polynomials Quantum groups Quantum theory Representations of algebras Representations of groups Representations of Lie groups Series Shaw, Run Run, Sheaf theory Singularities (Mathematics) Topological groups Vector bundles
Alternative Names
George Lusztig American mathematician and Abdun Nur Professor at the Massachusetts Institute of Technology (MIT)
George Lusztig Amerikaans wiskundige
George Lusztig amerikansk matematikar
George Lusztig amerikansk matematiker
George Lusztig matematician american
George Lusztig matematico statunitense
George Lusztig mathématicien américain
George Lusztig USamerikanischer Mathematiker
Lusztig, G.
Lusztig, G. 1946
Lusztig, George
Джордж Люстиґ
Люстиг, Джордж американский математик, профессор Массачусетског технологического института
ג'ורג' לוסטיג
ジョージ・ルスティック
喬治·盧斯蒂格
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