Generic stabilizers in actions of simple algebraic groups
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Lawther, Ross https://orcid.org/0000-0002-1484-5149
Guralnick, Robert M
Abstract
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, 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.
Description
Keywords
Journal Title
Memoirs of the American Mathematical Society
Conference Name
Journal ISSN
0065-9266
Volume Title
Publisher
American Mathematical Society