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

摘要

We define and study a class of spherical subgroups of a Kac-Moody group. Inanalogy with the standard theory of spherical varieties, we introduce acombinatorial object associated with such a subgroup, its homogeneous sphericaldatum, and we prove that it satisfies the same axioms as in thefinite-dimensional case. Our main tool is a study of varieties that arespherical under the action of a connected reductive group L, and come equippedwith a transitive action of a group containing L as a Levi subgroup.