WorldCat Identities

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
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Most widely held works about George Lusztig
 
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 semi-simple 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 Kac-Moody 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 Drinfeld-Jimbo 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 new-at 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

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
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

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 p-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) 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 KL-basis also possess very interestin
Iwahori-Hecke algebras and their representation theory : lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, June 28-July 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 Iwahori-Hecke 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 Iwahori-Hecke 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

Current developments in mathematics, 2002( Book )

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

Reductive group actions with one-dimensional quotient by Hanspeter Kraft( Book )

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

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

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

Analyse et topologie sur les espaces singuliers : CIRM, 6-10 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

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

Discrete Series of GLn Over a Finite Field. (AM-81) by George Lusztig( Book )

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. (AM-107) 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
Characters of Reductive Groups over a Finite Field. (AM-107) by George Lusztig( )

1 edition published in 1984 in English and held by 0 WorldCat member libraries worldwide

Discrete Series of GLn Over a Finite Field. (AM-81) by George Lusztig( )

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 June-15 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
 
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The discrete series of GLn over a finite field
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 US-amerikanischer 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

Languages
English (114)

French (5)

German (2)

Covers
The discrete series of GLn over a finite fieldCharacters of reductive groups over a finite fieldHecke algebras with unequal parametersIwahori-Hecke algebras and their representation theory : lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, June 28-July 6, 1999Current developments in mathematics, 2002