Branching laws for minimal holomorphic representations
Artikel i vetenskaplig tidskrift, 2007

In this paper we study the branching law for the restriction from SU (n, m) to SO (n, m) of the minimal representation in the analytic continuation of the scalar holomorphic discrete series. We identify the group decomposition with the spectral decomposition of the action of the Casimir operator on the subspace of S (O (n) × O (m))-invariants. The Plancherel measure of the decomposition defines an L 2 -space of functions, for which certain continuous dual Hahn polynomials furnish an orthonormal basis. It turns out that the measure has point masses precisely when n - m > 2. Under these conditions we construct an irreducible representation of SO (n, m), identify it with a parabolically induced representation, and construct a unitary embedding into the representation space for the minimal representation of SU (n, m). © 2007 Elsevier Inc. All rights reserved.

polynomials

transform

kernels

spaces

bounded symmetric domains

Författare

Henrik Seppänen

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Functional Analysis

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

Vol. 251 174-209

Ämneskategorier

Matematik

DOI

10.1016/j.jfa.2007.04.004