Principal series of Hermitian Lie groups induced from Heisenberg parabolic subgroups

摘要

Let G be an irreducible Hermitian Lie group and D = G/K its bounded symmetric domain in C-d of rank r. Each gamma of the Harish-Chandra strongly orthogonal roots {gamma(1), ..., gamma(r)} defines a Heisenberg parabolic subgroup P = MAN of G. We study the principal series representations Ind(P)(G)(1 (R) e(nu) (R) 1) of G induced from P. These representations can be realized as the L-2-space on the minimal K-orbit S = Ke = K/L of a root vector e of gamma in C-d, and S is a circle bundle over a compact Hermitian symmetric space K/L-0 of K of rank one or two. We find the complementary series, reduction points, and unitary sub-quotients in this family of representations. (C) 2022 The Author(s). Published by Elsevier Inc.