Strongly solvable spherical subgroups and their combinatorial invariants

TL;DR

This paper explores the relationships between three combinatorial classifications of strongly solvable spherical subgroups in reductive complex algebraic groups, providing detailed descriptions and interrelations to unify the classifications.

Contribution

It establishes connections between three major classifications of strongly solvable spherical subgroups, enabling translation between their combinatorial invariants.

Findings

Unified framework for classifications of strongly solvable spherical subgroups

Explicit relations between different combinatorial invariants

Facilitates transfer of results across classification schemes

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.