Hostname: page-component-cb9f654ff-65tv2 Total loading time: 0 Render date: 2025-08-27T00:55:32.020Z Has data issue: false hasContentIssue false
  • English
  • Français

A Weight Theory for Unitary Representations

Published online by Cambridge University Press:  20 November 2018

Thomas Sherman
Thomas Sherman*
Affiliation:
The Institute for Advanced Study, Princeton
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.

Over a field of characteristic 0 certain of the simple Lie algebras have a root theory, namely those called “split” in Jacobson's book (3). We shall assume some familiarity with the subject matter of this book. Then the finite-dimensional representations of these Lie algebras have a weight theory. Our purpose here is to present a kind of weight theory for the representations of these Lie algebras when their ground field is the real numbers, and when the representation comes from a unitary group representation.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 159 - 168
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Gelfand, I. and Naimark, M., Unitary representations of the group of linear transformations of the straight line, C. R. (Doklady), Acad. Sci. U.S.S.R. (N.S.), 55 (1947), 567–570.Google Scholar
2. Halmos, Paul, Introduction to Hilbert space and the theory of spectral multiplicity (New York, 1957).Google Scholar
3. Jacobson, Nathan, Lie algebras (New York, 1962).Google Scholar
4. Mackey, George W., A theorem of Stone and von Neumann, Duke Math J., 16 (1949), 313–326.Google Scholar
5. Mackey, George W., Induced representations of locally compact groups, I, Ann. of Math., 55 (1952), 101–139.Google Scholar
6. Nelson, Edward, Analytic vectors, Ann. of Math., 70 (1959), 572–615.Google Scholar
7. Segal, I. E., Hypermaximality of certain operators on Lie groups, Proc. Amer. Math. Soc, 8 (1952), 13–15.Google Scholar