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August 2022 Generic Stabilizers for Simple Algebraic Groups
Skip Garibaldi, Robert M. Guralnick
Michigan Math. J. 72: 343-387 (August 2022). DOI: 10.1307/mmj/20217216

Abstract

We prove a myriad of results related to the stabilizer in an algebraic group G of a generic vector in a representation V of G over an algebraically closed field k. Our results are on the level of group schemes, which carries more information than considering both the Lie algebra of G and the group G(k) of k-points. For G simple and V faithful and irreducible, we prove the existence of a stabilizer in general position, sometimes called a principal orbit type. We determine those G and V for which the stabilizer in general position is smooth, or dimV/G<dimG, or there is a vV whose stabilizer in G is trivial.

Dedication

To Gopal Prasad, in honor of his 75th birthday

Citation

Download Citation

Skip Garibaldi. Robert M. Guralnick. "Generic Stabilizers for Simple Algebraic Groups." Michigan Math. J. 72 343 - 387, August 2022. https://doi.org/10.1307/mmj/20217216

Information

Received: 28 May 2021; Revised: 14 November 2021; Published: August 2022
First available in Project Euclid: 2 August 2022

Digital Object Identifier: 10.1307/mmj/20217216

Subjects:
Primary: 20G05
Secondary: 14L24

Rights: Copyright © 2022 The University of Michigan

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Vol.72 • August 2022
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