Principal series of quaternionic and real split exceptional Lie groups induced from Heisenberg parabolic subgroups

2023/09/12 by Zhang, Genkai
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2309.05980

Abstract

Let G/K be an irreducible quaternionic symmetric space of rank 4. We study the principal series representation π_ν=Ind_P^G(1⊗ e^ν⊗ 1) of G induced from the Heisenberg parabolic subgroup P=MAN realized on L²(K/L), L=K∩ M. We find the K-types in the induced representation via a double cover K/L₀→ K/L and a circle bundle K/L₀→ K/L₁ over a compact Hermitian symmetric space K/L₁. We compute the Lie algebra \mathfrak g-action of G on the representation space. We find the complementary series, reducible points, and unitary subrepresentations in this family of representations.

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