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A note on branching theorems

Authors:	Kenneth D. Johnson

Affiliation:	Department of Mathematics, University of Georgia, Athens, Georgia 30602

Abstract:	Let be a complex, simply connected semisimple analytic group with a closed connected reductive subgroup. Suppose is an irreducible holomorphic -module and an irreducible holomorphic -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 . Moreover, $dimtext{Hom}_{K} (W,V)le 1$ for all and if and only if $U{(mathfrak{g})}^{K}$ is commutative.

Keywords:	Enveloping algebra centralizer module

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