Parabolically connected subgroups

TL;DR

This paper classifies certain reductive spherical subgroups of SL(n) with a specific connectivity property, ensuring their embeddings into Moishezon spaces are algebraic, thus contributing to the understanding of algebraic group actions.

Contribution

It provides a complete description of reductive spherical subgroups of SL(n) with connected intersections with parabolic subgroups, a novel classification result.

Findings

Classified all reductive spherical subgroups with the connectivity property.

Proved that such subgroups guarantee algebraic embeddings into Moishezon spaces.

Enhanced understanding of subgroup structures in SL(n).

Abstract

We describe all reductive spherical subgroups of the group SL(n) which have connected intersection with any parabolic subgroup of the group SL(n). This condition guarantees that any open equivariant embedding of the corresponding homogeneous space into a Moishezon space is algebraic.