Discrete branching laws for minimal holomorphic representations

Abstract

We find the explicit branching laws for the restriction of minimal holomorphic representations to symmetric subgroups in the case where the restriction is discretely decomposable. For holomorphic pairs the minimal holomorphic representation decomposes into a direct sum of lowest weight representations which is made explicit. For non-holomorphic pairs the restriction is shown to be irreducible and identified with a known representation. We further study a conjecture by Kobayashi on the behaviour of associated varieties under restriction and confirm this conjecture in the setting of this paper.

28 pages

References in corpus (1)

• Branching of some holomorphic representations of SO(2,N)

Cited by in corpus (4)

• Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval-Plancherel-Type Formulas under Subgroups
• Discrete series of simple Lie groups with admissible restriction to a $S{L}_2(\mathbb{R})$
• Restriction of irreducible unitary representations of Spin(N,1) to parabolic subgroups
• Kobayashi's conjecture on associated varieties for $({\mathrm{E}}_{6(-14)},\mathrm{Spin}(8,1))$