Virtual character modules of semisimple Lie groups and representations of Weyl groups (Q1073932)

Let G be a connected semi-simple acceptable Lie group with finite center. Denote the virtual character module of G whose elements have infinitesimal character \(\lambda\) by V(\(\lambda)\). For regular \(\lambda\) the author defines representations of the ''integral Weyl group W(\(\lambda)\)'' on a subspace \(V_ H(\lambda)\subset V(\lambda)\). In the case that \(\lambda\) is regular and integral \(W(\lambda)=W\), \(V_ H(\lambda)=V(\lambda)\) and the representations are canonically identified with those defined by G. Zuckerman using tensor products.