English

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

Representation Theory 2017-03-29 v3 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1408.3347,
  title  = {Spherical subgroups of Kac-Moody groups and transitive actions on spherical varieties},
  author = {Guido Pezzini},
  journal= {arXiv preprint arXiv:1408.3347},
  year   = {2017}
}

Comments

v2: Some changes in the introduction, and added a new section with a proof of Conjecture 17.1 of version 1; v3: Final version, corrections and additional details in several proofs