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.
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Noël, A.G. (2006). A General Computational Scheme for Testing Admissibility of Nilpotent Orbits of Real Lie Groups of Inner Type. In: Iglesias, A., Takayama, N. (eds) Mathematical Software - ICMS 2006. ICMS 2006. Lecture Notes in Computer Science, vol 4151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11832225_1
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DOI: https://doi.org/10.1007/11832225_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38084-9
Online ISBN: 978-3-540-38086-3
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