Cuspidal local systems and graded Hecke algebras. I
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 [\textit{D. Kazhdan}, \textit{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.].
scientific article; zbMATH DE number 4146302