Strongly solvable spherical subgroups and their combinatorial invariants

Abstract

A subgroup H of an algebraic group G is said to be strongly solvable if H is contained in a Borel subgroup of G. This paper is devoted to establishing relationships between the following three combinatorial classifications of strongly solvable spherical subgroups in reductive complex algebraic groups: Luna's general classification of arbitrary spherical subgroups restricted to the strongly solvable case, Luna's 1993 classification of strongly solvable wonderful subgroups, and the author's 2011 classification of strongly solvable spherical subgroups. We give a detailed presentation of all the three classifications and exhibit interrelations between the corresponding combinatorial invariants, which enables one to pass from one of these classifications to any other.

v3: 58 pages, revised according to the referee's suggestions; v4: numbering of sections changed to agree with the published version

References in corpus (4)

• Classification of smooth affine spherical varieties
• On solvable spherical subgroups of semisimple algebraic groups
• Normalizers of solvable spherical subgroups
• Localization of spherical varieties

Cited by in corpus (6)

• New and old results on spherical varieties via moduli theory
• Orbits of strongly solvable spherical subgroups on the flag variety
• Equivariant models of spherical varieties
• On extended weight monoids of spherical homogeneous spaces
• Real structures on symmetric spaces
• Degenerations of spherical subalgebras and spherical roots