## Cuspidal local systems and graded Hecke algebras. I.(English)Zbl 0699.22026

Hecke algebras of affine Weyl groups with equal parameters are important to representation theory of p-adic reductive groups because their simple modules give those representations that admit an Iwahori fixed vector. But also Hecke algebras with unequal parameters occur in representation theory, i.e. as endomorphism algebras of induced representations.
The paper is concerned with the graded version of H of such an algebra with respect to a natural filtration. Similar to [D. Kazhdan, G. Lusztig, Invent. Math. 87, 153-215 (1987; Zbl 0613.22004)] where affine Hecke algebras are treated, the algebra H is realized in equivariant homology of a generalized flag variety of G, where G is the complex Lie group attached to the root data defining H. Thus the simple H-modules are classified in a way similar to [loc. cit.].
Reviewer: A.Deitmar

### MSC:

 22E50 Representations of Lie and linear algebraic groups over local fields 14L30 Group actions on varieties or schemes (quotients) 20C07 Group rings of infinite groups and their modules (group-theoretic aspects) 14C35 Applications of methods of algebraic $$K$$-theory in algebraic geometry

Zbl 0613.22004
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### References:

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