k-Dirac Complexes
This is the first paper in a series of two papers. In this paper, we construct complexes of invariant differential operators that live on homogeneous spaces of |2|-graded parabolic geometries of some particular type. We call them k-Dirac complexes. More explicitly, we will show that each k-Dirac com...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2018 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2018
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209452 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | k-Dirac Complexes / T. Salač // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862723306920083456 |
|---|---|
| author | Salač, T. |
| author_facet | Salač, T. |
| citation_txt | k-Dirac Complexes / T. Salač // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This is the first paper in a series of two papers. In this paper, we construct complexes of invariant differential operators that live on homogeneous spaces of |2|-graded parabolic geometries of some particular type. We call them k-Dirac complexes. More explicitly, we will show that each k-Dirac complex arises as the direct image of a relative BGG sequence, and so this fits into the scheme of the Penrose transform. We will also prove that each k-Dirac complex is formally exact, i.e., it induces a long exact sequence of infinite (weighted) jets at any fixed point. In the second part of the series, we use this information to show that each k-Dirac complex is exact at the level of formal power series at any point and that it descends to a resolution of the k-Dirac operator studied in Clifford analysis.
|
| first_indexed | 2025-12-07T18:40:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209452 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:40:32Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Salač, T. 2025-11-21T19:04:49Z 2018 k-Dirac Complexes / T. Salač // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58J10; 32N05; 32L25; 35A22; 53C28; 58A20 arXiv: 1705.09469 https://nasplib.isofts.kiev.ua/handle/123456789/209452 https://doi.org/10.3842/SIGMA.2018.012 This is the first paper in a series of two papers. In this paper, we construct complexes of invariant differential operators that live on homogeneous spaces of |2|-graded parabolic geometries of some particular type. We call them k-Dirac complexes. More explicitly, we will show that each k-Dirac complex arises as the direct image of a relative BGG sequence, and so this fits into the scheme of the Penrose transform. We will also prove that each k-Dirac complex is formally exact, i.e., it induces a long exact sequence of infinite (weighted) jets at any fixed point. In the second part of the series, we use this information to show that each k-Dirac complex is exact at the level of formal power series at any point and that it descends to a resolution of the k-Dirac operator studied in Clifford analysis. The author is grateful to Vladimír Souček for his support and many useful conversations. The author would also like to thank Lukáš Krump for the possibility of using his package for the Young diagrams. The author wishes to thank the unknown referees for many helpful suggestions, which considerably improved this article. The research was partially supported by the grant 17-01171S of the Grant Agency of the Czech Republic. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications k-Dirac Complexes Article published earlier |
| spellingShingle | k-Dirac Complexes Salač, T. |
| title | k-Dirac Complexes |
| title_full | k-Dirac Complexes |
| title_fullStr | k-Dirac Complexes |
| title_full_unstemmed | k-Dirac Complexes |
| title_short | k-Dirac Complexes |
| title_sort | k-dirac complexes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209452 |
| work_keys_str_mv | AT salact kdiraccomplexes |