Spherical roots of spherical varieties

Abstract

Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this fundamental theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer's classification of spherical rank-1-varieties.

v1; 19 pages; v2: 19 pages, reformatted to LaTeX, slightly expanded, a couple of minor errors corrected; v3: 19 pages, minor modifications, final version

References in corpus (2)

• Power reductivity over an arbitrary base
• An introduction to wonderful varieties with many examples of type F4

Cited by in corpus (4)

• The dual group of a spherical variety
• Spherical subgroups in simple algebraic groups
• Intersection complexes and unramified $L$-factors
• K-stability and polystable degenerations of polarized spherical varieties