Degenerations of spherical subalgebras and spherical roots

Abstract

We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain one-parameter degenerations of the Lie algebras corresponding to such subgroups. As an application, we exhibit explicit algorithms for computing the set of spherical roots of such a spherical subgroup.

v3: 46 pages, revised in accordance with suggestions of several referees

References in corpus (3)

• Classification of smooth affine spherical varieties
• Uniqueness property for spherical homogeneous spaces
• On extended weight monoids of spherical homogeneous spaces

Cited by in corpus (1)

• Degenerations of nilpotent algebras