SPHERICAL ACTIONS ON ISOTROPIC FLAG VARIETIES AND RELATED BRANCHING RULES

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 irreducib...

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Bibliographic Details
Published in:Transformation groups 2021-09, Vol.26 (3), p.719-774
Main Authors: AVDEEV, ROMAN, PETUKHOV, ALEXEY
Format: Article
Language:English
Subjects:
Algebra
Flags
Lie Groups
Mathematics
Mathematics and Statistics
Subgroups
Topological Groups
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Summary: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 .
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-020-09593-1