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One more method to construct the irreducible unitary representations of nipotent Lie groups

Published online by Cambridge University Press:  09 April 2009

A. A. Astaneh
A. A. Astaneh
Affiliation:
Department of Mathematics, University of Mashhad, Mashhad, Iran
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Abstract

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In this paper one more canonical method to construct the irreducible unitary representations of a connected, simply connected nilpotent Lie group is introduced. Although we used Kirillov' analysis to deduce this procedure, the method obtained differs from that of Kirillov's, in that one does not need to consider the codjoint representation of the group in the dual of its Lie algebra (in fact, neither does one need to consider the Lie algebra of the group, provided one knows certain connected subgroups and their characters). The method also differs from that of Mackey's as one only needs to induce characters to obtain all irreducible representations of the group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 1 , February 1986 , pp. 89 - 94
Copyright
Copyright © Australian Mathematical Society 1986

References

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[3]Mackey, G. W., ‘Unitary representations of group extensions I’, Acta Math. 99 (1958), 265–311.CrossRefGoogle Scholar
[4]Pukanszky, L., Leçons sur les representations des groupes (Dunod, Paris, 1967).Google Scholar