Representations of Affine Hecke Algebras

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