# Degenerations of spherical subalgebras and spherical roots

## TL;DR

This paper studies the structure of certain spherical subgroups in complex algebraic groups, introduces degenerations of their Lie algebras, and provides algorithms to compute their spherical roots.

## Contribution

It extends the class of strongly solvable spherical subgroups and offers explicit algorithms for spherical root computation.

## Key findings

- Structural results for a broader class of spherical subgroups
- Construction of one-parameter degenerations of Lie algebras
- Algorithms for computing 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.