# Representations of Affine Hecke Algebras

Part of the Lecture Notes in Mathematics book series (LNM, volume 1587)

Part of the Lecture Notes in Mathematics book series (LNM, volume 1587)

Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra H*q* (*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 H*q*-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 H*q*-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

Abstract algebra Affine Hecke Algebras K-theory Representation algebra

- DOI https://doi.org/10.1007/BFb0074130
- Copyright Information Springer-Verlag Berlin Heidelberg 1994
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-58389-9
- Online ISBN 978-3-540-48682-4
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
- About this book