Principal series of Hermitian Lie groups induced from Heisenberg parabolic subgroups
Journal article, 2022

Let G be an irreducible Hermitian Lie group and D=G/K its bounded symmetric domain in Cd of rank r. Each γ of the Harish-Chandra strongly orthogonal roots {γ1,⋯,γr} defines a Heisenberg parabolic subgroup P=MAN of G. We study the principal series representations IndPG(1⊗eν⊗1) of G induced from P. These representations can be realized as the L2-space on the minimal K-orbit S=Ke=K/L of a root vector e of γ in Cd, and S is a circle bundle over a compact Hermitian symmetric space K/L0 of K of rank one or two. We find the complementary series, reduction points, and unitary sub-quotients in this family of representations.

Hermitian Lie groups

Induced representations

Heisenberg parabolic subgroups

Composition and Complementary series


Genkai Zhang

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 282 8 109399

Subject Categories

Mathematical Analysis



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