Orbits of strongly solvable spherical subgroups on the flag variety

Abstract

Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup H of B acting with finitely many orbits on the flag variety G/B, and we classify the H-orbits in G/B in terms of suitable combinatorial invariants. As well, we study the Weyl group action defined by Knop on the set of H-orbits in G/B, and we give a combinatorial model for this action in terms of weight polytopes.

v4: final version, to appear on Journal of Algebraic Combinatorics. Apported some minor corrections to the previous version

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Cited by in corpus (5)

• On extended weight monoids of spherical homogeneous spaces
• Spherical nilpotent orbits and abelian subalgebras in isotropy representations
• Root subgroups on affine spherical varieties
• P-flag spaces and incidence stratifications
• B_{n-1}-bundles on the flag variety, II