Proceedings of the Japan Academy, Series A, Mathematical Sciences

Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds

Hideko Sekiguchi

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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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Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 3 (2011), 31-34.

First available in Project Euclid: 3 March 2011

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Primary: 22E46: Semisimple Lie groups and their representations
Secondary: 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 20G05: Representation theory

Branching rule symmetric pair Penrose transform singular unitary representation


Sekiguchi, Hideko. Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 3, 31--34. doi:10.3792/pjaa.87.31.

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