A note on branching theorems
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- by Kenneth D. Johnson PDF
- Proc. Amer. Math. Soc. 129 (2001), 351-353 Request permission
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 351-353
- MSC (1991): Primary 17B35, 22E46; Secondary 22E10
- DOI: https://doi.org/10.1090/S0002-9939-00-05646-X
- MathSciNet review: 1709755