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Representations of Hecke algebras. (English) Zbl 0729.20016
Orbites unipotentes et représentations. I. Groupes finis et algèbres de Hecke, Astérisque 168, 13-60 (1988).

[For the entire collection see Zbl 0695.00014.]

Let G be a finite Chevalley group, W its Weyl group and H the generic Hecke algebra of W. The author discusses the impact of the positivity properties of the coefficients of the Kazhdan-Lusztig polynomials and the structure constants of H for the Kazhdan-Lusztig basis for the structure and representation theory of H. He reproves recent results of G. Lusztig using positivity results and some ideas from unpublished lecture notes by T. A. Springer.

MSC:
20G05Representation theory of linear algebraic groups
20F55Reflection groups; Coxeter groups
20C33Representations of finite groups of Lie type