Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds

Sekiguchi, Hideko

Proc. Japan Acad. Ser. A Math. Sci., Tome 87 (2011) no. 1, p. 31-34 / Harvested from Project Euclid

Résumé

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.

Publié le : 2011-03-15
Classification: Branching rule, symmetric pair, Penrose transform, singular unitary representation, 22E46, 05E15, 20G05

@article{1299161392,
     author = {Sekiguchi, Hideko},
     title = {Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {87},
     number = {1},
     year = {2011},
     pages = { 31-34},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1299161392}
}

Sekiguchi, Hideko. Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds. Proc. Japan Acad. Ser. A Math. Sci., Tome 87 (2011) no. 1, pp.  31-34. http://gdmltest.u-ga.fr/item/1299161392/