Enright-Shelton theory and Vogan's problem for generalized principal series / Brian D. Boe, David H. Collingwood

Let G be a connected semisimple Lie group with finite center and K its maximal compact subgroup. Let P be a parabolic subgroup of G and P=MAN its Langlands decomposition. Let σ be a discrete series representation of M and ν a (non-unitary) character of A. The induced Harish-Chandra module Ind P G (σ,ν) is called a generalized principal series representation. Generalized principal series are of finite length, and in the case of groups with real rank one, all of their irreducible constituents occur with multiplicity one. D. Vogan and B. Speh asked if generalized principal series representations corresponding to maximal parabolic subgroups always have multiplicity one. In this paper the authors study in great details the composition series of such generalized principal series representations for groups with Hermitian symmetric space G/K. Among other results, they show that these representations are not necessarily multiplicity free in the case of real symplectic groups. (Zentralblatt)

Bibliogr. p. 106-107