Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T00:57:05.559Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Unitarized Adjoint Representation of a Semisimple Lie Group II

Published online by Cambridge University Press:  20 November 2018

Ronald L. Lipsman
Ronald L. Lipsman*
Affiliation:
University of Maryland, College Park, Maryland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a connected semisimple Lie group with Lie algebra . Lebesgue measure on is invariant under the adjoint action of G; and so there is a natural unitary representation TG of G on L2 given by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1217 - 1222
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Helgason, S., Differential geometry and symmetric spaces (Academic Press, New York, 1962).Google Scholar
2. Lipsman, R., Group representations (Springer-Verlag Lecture Notes in Mathematics, no. 388, 1974).Google Scholar
3. Lipsman, R. On the unitary representation of a semisimple Lie group given by the invariant integral on its Lie algebra, Advances in Math., to appear.Google Scholar
4. Lipsman, R. On the unitarized adjoint representation of a semisimple Lie group III, to appear.Google Scholar