Spherical actions on isotropic flag varieties and related branching rules

Abstract

Let $G$ be a symplectic or special orthogonal group, let $H$ be a connected reductive subgroup of $G$, and let $X$ be a flag variety of $G$. We classify all triples $(G,H,X)$ such that the natural action of $H$ on $X$ is spherical. For each of these triples, we determine the restrictions to $H$ of all irreducible representations of $G$ realized in spaces of sections of homogeneous line bundles on $X$.

v4: 51 pages, updated references and a few minor changes

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• Uniformly bounded multiplicities, polynomial identities and coisotropic actions