**CRM Monograph Series**

Volume: 18;
2003;
136 pp;
Hardcover

MSC: Primary 20;
**Print ISBN: 978-0-8218-3356-8
Product Code: CRMM/18**

List Price: $46.00

Individual Member Price: $36.80

# Hecke Algebras with Unequal Parameters

Share this page
*G. Lusztig*

A co-publication of the AMS and Centre de Recherches Mathématiques

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 interesting combinatorial properties.

In the present book, the author extends the theory of the KL-basis to a
more general class of Hecke algebras, the so-called algebras with
unequal parameters. In particular, he formulates conjectures describing
the properties of Hecke algebras with unequal parameters and presents
examples verifying these conjectures in particular cases.

Written in the author's precise style, the book gives researchers and
graduate students working in the theory of algebraic groups and their
representations an invaluable insight and a wealth of new and useful
information.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Table of Contents

# Table of Contents

## Hecke Algebras with Unequal Parameters

#### Readership

Graduate students and research mathematicians interested in group theory and generalizations.