Abstract

Inspired by work of Enright and Willenbring, we prove a generalized Littlewood’s restriction formula in terms of Dirac cohomology. Our approach is to use a character formula of irreducible unitary lowest weight modules instead of the Bernstein-Gelfand-Gelfand resolution, and the proof is much simpler. We also show that our branching formula is equivalent to the formula of Enright and Willenbring in terms of nilpotent Lie algebra cohomology. This follows from the close relationship between the Dirac cohomology and the corresponding nilpotent Lie algebra cohomology for unitary representations of semisimple Lie groups of Hermitian type, which was established by Huang, Pandzic, and Renard.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1253-1269
Launched on MUSE
2013-09-25
Open Access
No
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