Borel-Weil factorization for super Grassmannians
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912864508313600 |
|---|---|
| author | Sam, Steven V |
| author_facet | Sam, Steven V |
| contents | This article deals with computing the cohomology of Schur functors applied to tautological bundles on super Grassmannians. We show that in a range of cases, the cohomology is a free module over the cohomology of the structure sheaf and that the space of generators is an irreducible representation of the general linear supergroup that can be constructed via explicit multilinear operations. Our techniques come from commutative algebra: we relate this cohomology calculation to Tor groups of certain algebraic varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Borel-Weil factorization for super Grassmannians Sam, Steven V Representation Theory Commutative Algebra Algebraic Geometry 17B10, 14M30 This article deals with computing the cohomology of Schur functors applied to tautological bundles on super Grassmannians. We show that in a range of cases, the cohomology is a free module over the cohomology of the structure sheaf and that the space of generators is an irreducible representation of the general linear supergroup that can be constructed via explicit multilinear operations. Our techniques come from commutative algebra: we relate this cohomology calculation to Tor groups of certain algebraic varieties. |
| title | Borel-Weil factorization for super Grassmannians |
| topic | Representation Theory Commutative Algebra Algebraic Geometry 17B10, 14M30 |
| url | https://arxiv.org/abs/2407.05167 |