Spherical roots of spherical varieties
Copyright policy )Spherical roots of spherical varieties
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 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 varieties of rank 1.
Group actions on varieties or schemes (quotients), 14M27, 14L30, 14G17, spherical varieties, Positive characteristic ground fields in algebraic geometry, Mathematics - Algebraic Geometry, spherical roots, FOS: Mathematics, fields of positive characteristic, Compactifications; symmetric and spherical varieties, Representation Theory (math.RT), homogeneous varieties, Algebraic Geometry (math.AG), Mathematics - Representation Theory
Group actions on varieties or schemes (quotients), 14M27, 14L30, 14G17, spherical varieties, Positive characteristic ground fields in algebraic geometry, Mathematics - Algebraic Geometry, spherical roots, FOS: Mathematics, fields of positive characteristic, Compactifications; symmetric and spherical varieties, Representation Theory (math.RT), homogeneous varieties, Algebraic Geometry (math.AG), Mathematics - Representation Theory
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