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Introduction to Quantum Groups (Paperback, 1st ed. 1993. Corr. 2nd printing 1994. 3rd. printing 2010): George Lusztig Introduction to Quantum Groups (Paperback, 1st ed. 1993. Corr. 2nd printing 1994. 3rd. printing 2010)
George Lusztig
R2,440 Discovery Miles 24 400 Ships in 10 - 15 working days

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

Iwahori-Hecke Algebras and their Representation Theory - Lectures given at the CIME Summer School held in Martina Franca,... Iwahori-Hecke Algebras and their Representation Theory - Lectures given at the CIME Summer School held in Martina Franca, Italy, June 28 - July 6, 1999 (Paperback, 2002 ed.)
Ivan Cherednik; Edited by Dan Barbasch; Yavor Markov; Edited by M. Welleda Baldoni; Roger E. Howe, …
R1,348 Discovery Miles 13 480 Ships in 10 - 15 working days

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.

Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 (Paperback): George Lusztig Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 (Paperback)
George Lusztig
R1,479 R1,335 Discovery Miles 13 350 Save R144 (10%) Ships in 12 - 17 working days

In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes. The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2--1)...(qn-1--1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation ? of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq).

Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 (Paperback): George Lusztig Characters of Reductive Groups over a Finite Field. (AM-107), Volume 107 (Paperback)
George Lusztig
R2,863 R2,673 Discovery Miles 26 730 Save R190 (7%) Ships in 12 - 17 working days

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.

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