## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds

Hideko Sekiguchi

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 3 March 2011

https://projecteuclid.org/euclid.pja/1299161392

Digital Object Identifier
doi:10.3792/pjaa.87.31

Mathematical Reviews number (MathSciNet)
MR2802604

Zentralblatt MATH identifier
1227.22017

#### Citation

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. https://projecteuclid.org/euclid.pja/1299161392

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