Representations of Affine Hecke Algebras

1. Front Matter

   Pages I-VIII

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2. Hecke algebras

   • Nanhua Xi

   Pages 1-17

3. Affine Weyl groups and affine Hecke algebras

   • Nanhua Xi

   Pages 18-26

4. A generalized two-sided cell of an affine Weyl group

   • Nanhua Xi

   Pages 27-43

5. qs-analogue of weight multiplicity

   • Nanhua Xi

   Pages 44-47

6. Kazhdan-Lusztig classification on simple modules of affine Hecke algebras

   • Nanhua Xi

   Pages 48-62

7. An equivalence relation in T × ℂ^*

   • Nanhua Xi

   Pages 63-79

8. The lowest two-sided cell

   • Nanhua Xi

   Pages 80-84

9. Principal series representations and induced modules

   • Nanhua Xi

   Pages 85-92

10. Isogenous affine Hecke algebras

    • Nanhua Xi

    Pages 93-98

11. Quotient algebras

    • Nanhua Xi

    Pages 99-101

12. The based rings of cells in affine Weyl groups of type \(\widetilde{G_2 },\widetilde{B_2 },\widetilde{A_2 }\)

    • Nanhua Xi

    Pages 102-115

13. Simple modules attached to c ₁

    • Nanhua Xi

    Pages 116-128

14. Back Matter

    Pages 129-139

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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

• Abstract algebra
• Affine Hecke Algebras
• K-theory
• Representation
• algebra

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