Containment Relations among Spherical Subgroups

2018/04/02 by Hofscheier, Johannes
#20G05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14M27 #Representation Theory (math.RT) #Secondary 14L30

paper · doi:10.48550/arxiv.1804.00378

Abstract

A closed subgroup H of a connected reductive group G is called spherical if a Borel subgroup in G has an open orbit on G/H. We give a combinatorial characterization for a spherical subgroup to be contained in another one which generalizes previous work by Knop. As an application, we compute the Luna datum of the identity component of a spherical subgroup which yields a characterization of connectedness for spherical subgroups.

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