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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on branching theorems


Author: Kenneth D. Johnson
Journal: Proc. Amer. Math. Soc. 129 (2001), 351-353
MSC (1991): Primary 17B35, 22E46; Secondary 22E10
Published electronically: July 27, 2000
MathSciNet review: 1709755
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Abstract: Let $G$ be a complex, simply connected semisimple analytic group with $K$ a closed connected reductive subgroup. Suppose $V$ is an irreducible holomorphic $G$-module and $W$ an irreducible holomorphic $K$-module. We prove that Hom$_{K}(W,V)$ possesses the structure of an irreducible $U(\mathfrak{g})^{K}$-module whenever $\text{Hom}_{K}(W,V)$ is $\neq (0)$. Moreover, $\dim\text{Hom}_{K} (W,V)\le 1$ for all $W$ and $V$ if and only if $U{(\mathfrak{g})}^{K}$ is commutative.


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Additional Information

Kenneth D. Johnson
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: ken@alpha.math.uga.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05646-X
PII: S 0002-9939(00)05646-X
Keywords: Enveloping algebra, centralizer, module
Received by editor(s): September 1, 1998
Received by editor(s) in revised form: April 22, 1999
Published electronically: July 27, 2000
Communicated by: Roe Goodman
Article copyright: © Copyright 2000 American Mathematical Society