Representations of Affine Hecke Algebras
Title | Representations of Affine Hecke Algebras PDF eBook |
Author | Nanhua Xi |
Publisher | Springer |
Pages | 147 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 3540486828 |
Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest
Representations of Hecke Algebras at Roots of Unity
Title | Representations of Hecke Algebras at Roots of Unity PDF eBook |
Author | Meinolf Geck |
Publisher | Springer Science & Business Media |
Pages | 410 |
Release | 2011-05-18 |
Genre | Mathematics |
ISBN | 0857297163 |
The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.
Representations of Affine Hecke Algebras
Title | Representations of Affine Hecke Algebras PDF eBook |
Author | N. Xi |
Publisher | |
Pages | |
Release | 1993 |
Genre | |
ISBN |
Double Affine Hecke Algebras
Title | Double Affine Hecke Algebras PDF eBook |
Author | Ivan Cherednik |
Publisher | Cambridge University Press |
Pages | 449 |
Release | 2005-03-21 |
Genre | Mathematics |
ISBN | 0521609186 |
This is an essentially self-contained monograph centered on the new double Hecke algebra technique.
Iwahori-Hecke Algebras and Their Representation Theory
Title | Iwahori-Hecke Algebras and Their Representation Theory PDF eBook |
Author | Ivan Cherednik |
Publisher | Springer Science & Business Media |
Pages | 132 |
Release | 2002-12-19 |
Genre | Mathematics |
ISBN | 9783540002246 |
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.
Affine Hecke Algebras and Orthogonal Polynomials
Title | Affine Hecke Algebras and Orthogonal Polynomials PDF eBook |
Author | I. G. Macdonald |
Publisher | Cambridge University Press |
Pages | 200 |
Release | 2003-03-20 |
Genre | Mathematics |
ISBN | 9780521824729 |
First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.
On Representations of Affine Hecke Algebras
Title | On Representations of Affine Hecke Algebras PDF eBook |
Author | Jonathan Kusilek |
Publisher | |
Pages | |
Release | 2014 |
Genre | Hecke algebras |
ISBN |