Generic stabilizers in actions of simple algebraic groups

Fuente: arXiv
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Main Authors: Guralnick, R. M., Lawther, R.
Format: Preprint
Published: 2019
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author Guralnick, R. M.
Lawther, R.
author_facet Guralnick, R. M.
Lawther, R.
contents In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception (only in characteristic 2), there is a dense open subset any point of which has stabilizer conjugate to a fixed subgroup, called the generic stabilizer. We provide tables listing generic stabilizers in the cases where they are non-trivial; in addition we decide whether or not there is a dense orbit, or a regular orbit for the action on the module.
format Preprint
id arxiv_https___arxiv_org_abs_1904_13375
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle Generic stabilizers in actions of simple algebraic groups
Guralnick, R. M.
Lawther, R.
Group Theory
Algebraic Geometry
20G05
In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception (only in characteristic 2), there is a dense open subset any point of which has stabilizer conjugate to a fixed subgroup, called the generic stabilizer. We provide tables listing generic stabilizers in the cases where they are non-trivial; in addition we decide whether or not there is a dense orbit, or a regular orbit for the action on the module.
title Generic stabilizers in actions of simple algebraic groups
topic Group Theory
Algebraic Geometry
20G05
url https://arxiv.org/abs/1904.13375