Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians
We consider faithful actions of simple algebraic groups on self-dual irreducible modules and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the dimension of the variety. We prove that in all but a finite list of...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
|
| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001543/type/journal_article |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832589900894961664 |
|---|---|
| author | Aluna Rizzoli |
| author_facet | Aluna Rizzoli |
| author_sort | Aluna Rizzoli |
| collection | DOAJ |
| description | We consider faithful actions of simple algebraic groups on self-dual irreducible modules and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the dimension of the variety. We prove that in all but a finite list of cases, there is a dense open subset where the stabilizer of any point is conjugate to a fixed subgroup, called the generic stabilizer. We use these results to determine whether there exists a dense orbit. This in turn lets us complete the answer to the problem of determining all pairs of maximal connected subgroups of a classical group with a dense double coset. |
| format | Article |
| id | doaj-art-4280282f5527458cbb4ff4438c1bd1a4 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-4280282f5527458cbb4ff4438c1bd1a42025-01-24T05:20:20ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2024.154Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic GrassmanniansAluna Rizzoli0https://orcid.org/0000-0003-1501-3501King’s College London, Strand, London WC2R 2LS, UK;We consider faithful actions of simple algebraic groups on self-dual irreducible modules and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the dimension of the variety. We prove that in all but a finite list of cases, there is a dense open subset where the stabilizer of any point is conjugate to a fixed subgroup, called the generic stabilizer. We use these results to determine whether there exists a dense orbit. This in turn lets us complete the answer to the problem of determining all pairs of maximal connected subgroups of a classical group with a dense double coset.https://www.cambridge.org/core/product/identifier/S2050509424001543/type/journal_article14L3014M15 |
| spellingShingle | Aluna Rizzoli Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians Forum of Mathematics, Sigma 14L30 14M15 |
| title | Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians |
| title_full | Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians |
| title_fullStr | Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians |
| title_full_unstemmed | Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians |
| title_short | Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians |
| title_sort | generic stabilizers for simple algebraic groups acting on orthogonal and symplectic grassmannians |
| topic | 14L30 14M15 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001543/type/journal_article |
| work_keys_str_mv | AT alunarizzoli genericstabilizersforsimplealgebraicgroupsactingonorthogonalandsymplecticgrassmannians |