Author	Xi, Nanhua. author
Title	Representations of Affine Hecke Algebras [electronic resource] / by Nanhua Xi
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1994
Connect to	http://dx.doi.org/10.1007/BFb0074130
Descript	VIII, 144 p. online resource

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

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 ร ?* -- 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

1. Mathematics
2. Group theory
3. K-theory
4. Topological groups
5. Lie groups
6. Mathematics
7. Topological Groups
8. Lie Groups
9. Group Theory and Generalizations
10. K-Theory