Spherical subgroups of Kac-Moody groups and transitive actions on spherical varieties

TL;DR

This paper extends the theory of spherical varieties to Kac-Moody groups by defining spherical subgroups, introducing associated combinatorial data, and proving they satisfy finite-dimensional axioms, thus broadening the understanding of infinite-dimensional group actions.

Contribution

It introduces a framework for spherical subgroups of Kac-Moody groups, including a combinatorial classification analogous to finite-dimensional cases.

Findings

Defined spherical subgroups of Kac-Moody groups

Established combinatorial data satisfying finite-dimensional axioms

Analyzed varieties with transitive actions involving Levi subgroups

Abstract

We define and study a class of spherical subgroups of a Kac-Moody group. In analogy with the standard theory of spherical varieties, we introduce a combinatorial object associated with such a subgroup, its homogeneous spherical datum, and we prove that it satisfies the same axioms as in the finite-dimensional case. Our main tool is a study of varieties that are spherical under the action of a connected reductive group L, and come equipped with a transitive action of a group containing L as a Levi subgroup.