Representations of Hecke algebras on virtual character modules of a semisimple Lie group (Q1820252)

Let G be a connected semisimple acceptable Lie group with finite center, and denote by V(\(\chi)\) the complex vector space spanned by the characters of irreducible Harish-Chandra modules with infinitesimal character \(\chi\). Then V(\(\chi)\) is a direct sum of subspaces \(V_ H(\lambda)\) indexed by the conjugacy classes of Cartan subgroups H. For a pair ([H],\(\chi)\) the author defines a Hecke algebra \({\mathcal H}\) and a representation of \({\mathcal H}\) on \(V_ H(\chi)\). If the infinitesimal character is regular this representation can be identified with the representation of an integral Weyl group \(W_ H(\chi)\) on \(V_ H(\chi)\) defined by the author in a previous paper. Detailed proofs are to appear elsewhere.