A Weight Theory for Unitary Representations
- 1 January 1966
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 18, 159-168
- https://doi.org/10.4153/cjm-1966-020-0
Abstract
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.Keywords
This publication has 4 references indexed in Scilit:
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- Hypermaximality of certain operators on Lie groupsProceedings of the American Mathematical Society, 1952
- A theorem of Stone and von NeumannDuke Mathematical Journal, 1949