Wonderful subgroups of reductive groups and spherical systems
Abstract
Let G be a semisimple complex algebraic group, and H a wonderful subgroup of G. We prove several results relating the subgroup H to the properties of a combinatorial invariant S of G/H, called its spherical system. It is also possible to consider a spherical system S as a datum defined by purely combinatorial axioms, and under certain circumstances our results prove the existence of a wonderful subgroup H associated to S. As a byproduct, we reduce for any group G the proof of the classification of wonderful G-varieties, known as the Luna conjecture, to its verification on a small family of cases, called primitive.
Cite
@article{arxiv.1103.0380,
title = {Wonderful subgroups of reductive groups and spherical systems},
author = {Paolo Bravi and Guido Pezzini},
journal= {arXiv preprint arXiv:1103.0380},
year = {2014}
}
Comments
v1: 34 pages, this is the first of three papers which are going to supersede arXiv:0909.3771; v2: 39 pages, revised version accepted for publication in Journal of Algebra