Barbasch, Dan; Vogan, David Weyl group representations and nilpotent orbits. (English) Zbl 0537.22013 Representation theory of reductive groups, Proc. Conf., Park City/Utah 1982, Prog. Math. 40, 21-33 (1983). [For the entire collection see Zbl 0516.00013..] The authors study the real rank groups. In section 2 they parametrize the representations with a fixed regular integral infinitesimal character. Then the coherent continuation representation is studied and the notion of a cell is introduced. In section 3 some results on asymptotic support are given in order to calculate it for a special class of representations. Finally, the calculations are applied to U(p,q). Reviewer: C.Udrişte Cited in 15 Documents MSC: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) Keywords:Weyl group representations; nilpotent orbits; primitive ideals; enveloping algebra; Fourier inversion; unipotent orbital integrals; regular integral infinitesimal character; irreducible admissible (n,K) modules; wave front set; asymptotic support; cells Citations:Zbl 0516.00013 PDFBibTeX XML