A complex for the Dirac operator in several variables in dimension $4$
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913193616474112 |
|---|---|
| author | Krump, Lukáš Souček, Vladimír |
| author_facet | Krump, Lukáš Souček, Vladimír |
| contents | The Penrose transform was used to construct a complex starting with the Dirac operator in $k$ Clifford variables in dimension $2n$ in the stable range $n\geq k.$ In the paper, we consider the same Penrose transform in the special case of dimension $4$ and for any number of variables (i.e., in the nonstable range). In this case, we describe explicitely the corresponding relative BGG complex and its direct image for cohomology with values in a suitable line bundle (in singular infinitesimal character). We show that how to construct then a complex starting with the Dirac operator in any number of variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A complex for the Dirac operator in several variables in dimension $4$ Krump, Lukáš Souček, Vladimír Differential Geometry Representation Theory The Penrose transform was used to construct a complex starting with the Dirac operator in $k$ Clifford variables in dimension $2n$ in the stable range $n\geq k.$ In the paper, we consider the same Penrose transform in the special case of dimension $4$ and for any number of variables (i.e., in the nonstable range). In this case, we describe explicitely the corresponding relative BGG complex and its direct image for cohomology with values in a suitable line bundle (in singular infinitesimal character). We show that how to construct then a complex starting with the Dirac operator in any number of variables. |
| title | A complex for the Dirac operator in several variables in dimension $4$ |
| topic | Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2401.06554 |