A General Computational Scheme for Testing Admissibility of Nilpotent Orbits of Real Lie Groups of Inner Type

Abstract

One of the most fundamental problems in the field of Representation Theory is the description of all the unitary representations of a given group. For non-compact real reductive Lie groups, there is evidence that new unitary representations can be obtained from data provided by their admissible nilpotent orbits. In this paper, we describe a general scheme for determining the admissibility of a given real nilpotent orbit. We implement some parts of the scheme using the software system LiE. We give a detailed example and study the complexity of the algorithms.