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March 2011 Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds
Hideko Sekiguchi
Proc. Japan Acad. Ser. A Math. Sci. 87(3): 31-34 (March 2011). DOI: 10.3792/pjaa.87.31

Abstract

We consider a family of singular unitary representations which are realized in Dolbeault cohomology groups over indefinite Grassmannian manifolds, and find a closed formula of irreducible decompositions with respect to reductive symmetric pairs $(A_{2n-1}, D_{n})$. The resulting branching rule is a multiplicity-free sum of infinite dimensional, irreducible representations.

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Hideko Sekiguchi. "Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds." Proc. Japan Acad. Ser. A Math. Sci. 87 (3) 31 - 34, March 2011. https://doi.org/10.3792/pjaa.87.31

Information

Published: March 2011
First available in Project Euclid: 3 March 2011

zbMATH: 1227.22017
MathSciNet: MR2802604
Digital Object Identifier: 10.3792/pjaa.87.31

Subjects:
Primary: 22E46
Secondary: 05E15 , 20G05

Keywords: branching rule , Penrose transform , singular unitary representation , symmetric pair

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 3 • March 2011
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