Geodesic
A Weight Theory for Unitary Representations
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 159-168

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Sherman, Thomas. A Weight Theory for Unitary Representations. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 159-168. doi: 10.4153/CJM-1966-020-0
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