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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209452 |
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| 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| Zusammenfassung: | 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.
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| ISSN: | 1815-0659 |