Toric-friendly groups

TL;DR

This paper classifies semisimple connected linear algebraic groups over fields that have a unique orbit property for maximal tori, called toric-friendly groups, extending understanding of their structure.

Contribution

It provides a classification of semisimple (and under certain conditions, connected) toric-friendly groups over fields, a new property in algebraic group theory.

Findings

Classification of semisimple toric-friendly groups achieved

Identification of conditions under which connected groups are toric-friendly

Extension of the concept to certain connected groups under specific assumptions

Abstract

Let G be a connected linear algebraic group over a field k. We say that G is toric-friendly if for any field extension K/k and any maximal K-torus T in G the group G(K) has only one orbit in (G/T)(K). Our main result is a classification of semisimple (and under certain assumptions on k, of connected) toric-friendly groups.