Normalizers of solvable spherical subgroups

TL;DR

This paper computes the normalizer of any connected solvable spherical subgroup within a semisimple algebraic group, completing the classification of all such subgroups, whether connected or not.

Contribution

It provides a comprehensive calculation of the normalizers of solvable spherical subgroups, advancing the classification of these subgroups in semisimple algebraic groups.

Findings

Explicit description of N_G(H) for any connected solvable spherical subgroup H

Complete classification of all solvable spherical subgroups in semisimple algebraic groups

Extension of classification to non-connected subgroups

Abstract

For an arbitrary connected solvable spherical subgroup H of a connected semisimple algebraic group G we compute the group N_G(H), the normalizer of H in G. Thereby we complete a classification of all (not necessarily connected) solvable spherical subgroups in semisimple algebraic groups.