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arXiv · 1812.00936

Spherical actions on isotropic flag varieties and related branching rules

Roman Avdeev·Alexey Petukhov
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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 $X$.

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Roman Avdeev, Alexey Petukhov. 2018-12-03. Spherical actions on isotropic flag varieties and related branching rules. https://doi.org/10.1007/s00031-020-09593-1

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