Representations of Affine Hecke Algebras / by Nanhua Xi.

Format:

Book

Author/Creator:

Xi, Nanhua, 1963- author.

Contributor:

SpringerLink (Online service)

Series:

Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn ; 1587.

Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn ; 1587

Language:

English

Subjects (All):

Topological groups.

Group theory.

K-theory.

Topological Groups, Lie Groups.

Group Theory and Generalizations.

K-Theory.

Local Subjects:

Topological Groups, Lie Groups.

Group Theory and Generalizations.

K-Theory.

Physical Description:

1 online resource (VIII, 144 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994.

System Details:

text file PDF

Summary:

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.

Contents:

Hecke algebras

Affine Weyl groups and affine Hecke algebras

A generalized two-sided cell of an affine Weyl group

qs-analogue of weight multiplicity

Kazhdan-Lusztig classification on simple modules of affine Hecke algebras

An equivalence relation in T × ?*

The lowest two-sided cell

Principal series representations and induced modules

Isogenous affine Hecke algebras

Quotient algebras

The based rings of cells in affine Weyl groups of type

Simple modules attached to c 1.

Other Format:

Printed edition:

ISBN:

9783540486824

Access Restriction:

Restricted for use by site license.