Xi Representations of Affine Hecke Algebras

1994
ISBN: 978-3-540-48682-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 144 Seiten, eBook

Reihe: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn

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

Zielgruppe

Research

Autoren/Hrsg.

Xi, Nanhua

Inhaltsverzeichnis

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.