| Title:
|
Penrose transform and monogenic sections (English) |
| Author:
|
Salač, Tomáš |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
399-410 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Penrose transform gives an isomorphism between the kernel of the $2$-Dirac operator over an affine subset and the third sheaf cohomology group on the twistor space. In the paper we give an integral formula which realizes the isomorphism and decompose the kernel as a module of the Levi factor of the parabolic subgroup. This gives a new insight into the structure of the kernel of the operator. (English) |
| Keyword:
|
Penrose transform |
| Keyword:
|
monogenic spinors |
| MSC:
|
35A22 |
| MSC:
|
58J10 |
| idMR:
|
MR3007621 |
| DOI:
|
10.5817/AM2012-5-399 |
| . |
| Date available:
|
2012-12-17T14:04:37Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143114 |
| . |
| Reference:
|
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| Reference:
|
[2] Baston, R. J., Eastwood, M.: The Penrose transform – its interaction with representation theory.Oxford University Press, 1989. Zbl 0726.58004, MR 1038279 |
| Reference:
|
[3] Čap, A., Slovák, J.: Parabolic Geometries I, Background and General Theory.American Mathematical Society, Providence, 2009. Zbl 1183.53002, MR 2532439 |
| Reference:
|
[4] Colombo, F., Sabadini, I., Sommen, F., Struppa, D. C.: Analysis of Dirac Systems and Computational Algebra.Birkhäauser, Boston, 2004. Zbl 1064.30049, MR 2089988 |
| Reference:
|
[5] Franek, P.: Generalized Dolbeault Sequences in Parabolic Geometry.J. Lie Theory 18 (4) (2008), 757–773. Zbl 1176.17003, MR 2523135 |
| Reference:
|
[6] Goodman, R., Wallach, N. R.: Representations and Invariants of the Classical Groups.Cambridge University Press, 1998. Zbl 0901.22001, MR 1606831 |
| Reference:
|
[7] Krump, L., Salač, T.: Exactness of the Generalized Dolbeault Complex for k Dirac Operators in the Stable Rank.Numerical Analysis and Applied Mathematics ICNAAM, vol. 1479, 2012, pp. 300–303. |
| Reference:
|
[8] Salač, T.: k-Dirac operators and parabolic geometries.arXiv:1201.0355, 2012. |
| Reference:
|
[9] Salač, T.: The generalized Dolbeault complexes in Clifford analysis.Ph.D. thesis, MFF UK UUK, Prague, 2012. |
| Reference:
|
[10] Ward, R. S., Wells, R. O., Jr., : Twistor Geometry and Field.Cambridge University Press, 1990. MR 1054377 |
| . |
