Multiplicity in restricting minimal representations

TL;DR

This paper investigates how minimal representations of real reductive Lie groups behave when restricted to subgroups, establishing a bounded multiplicity property for these restrictions across various symmetric pairs.

Contribution

It proves a bounded multiplicity property for the restriction of minimal representations to arbitrary reductive symmetric pairs, advancing understanding of representation restrictions.

Findings

Bounded multiplicity property established for minimal representations

Applicable to arbitrary reductive symmetric pairs

Enhances understanding of representation restriction behavior

Abstract

We discuss the action of a subgroup on small nilpotent orbits, and prove a bounded multiplicity property for the restriction of minimal representations of real reductive Lie groups with respect to arbitrary reductive symmetric pairs.