Containment Relations among Spherical Subgroups

Containment Relations among Spherical Subgroups

A closed subgroup \(H\) of a connected reductive group \(G\) is called \(\textit{spherical}\) 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 app...

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Veröffentlicht in:arXiv.org 2018-04
1. Verfasser: Hofscheier, Johannes
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Combinatorial analysis
Containment
Datum (elevation)
Subgroups
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description A closed subgroup \(H\) of a connected reductive group \(G\) is called \(\textit{spherical}\) 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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subjects Combinatorial analysis
Containment
Datum (elevation)
Subgroups
title Containment Relations among Spherical Subgroups
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