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Published in:
2006 | OriginalPaper | Chapter
A General Computational Scheme for Testing Admissibility of Nilpotent Orbits of Real Lie Groups of Inner Type
Author : Alfred G. Noël
Published in: Mathematical Software - ICMS 2006
Publisher: Springer Berlin Heidelberg
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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.