| Title:
|
Symplectic twistor operator and its solution space on ${\mathbb{R}}^2$ (English) |
| Author:
|
Dostálová, Marie |
| Author:
|
Somberg, Petr |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
161-185 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the symplectic twistor operator $T_s$ in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension 1. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on ${\mathbb{R}}^2$. (English) |
| Keyword:
|
symplectic spin geometry |
| Keyword:
|
metaplectic Howe duality |
| Keyword:
|
symplectic twistor operator |
| Keyword:
|
symplectic Dirac operator |
| MSC:
|
53C27 |
| MSC:
|
53D05 |
| MSC:
|
81R25 |
| idZBL:
|
Zbl 06321156 |
| idMR:
|
MR3144180 |
| DOI:
|
10.5817/AM2013-3-161 |
| . |
| Date available:
|
2013-12-02T11:23:58Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143530 |
| . |
| Reference:
|
[1] Baum, H., Friedrich, T., Kath., I., Gruenewald, F.: Twistors and Killing Spinors on Riemannian Manifolds.B.G. Teubner, 1991. |
| Reference:
|
[2] Bie, H. De, Somberg, P., Souček, V.: The Howe Duality and Polynomial Solutions for the Symplectic Dirac Operator.Archive http://arxiv.org/pdf/1002.1053v1.pdf. |
| Reference:
|
[3] Britten, D. J., Lemire, F. W.: On modules of bounded multiplicities for the symplectic algebras.Trans. Amer. Math. Soc. 351 (1999), 3413–3431. Zbl 0930.17005, MR 1615943, 10.1090/S0002-9947-99-02338-7 |
| Reference:
|
[4] Crumeyrolle, A.: Orthogonal and Symplectic Clifford Algebras: Spinor Structures.Springer Netherlands, 2009. MR 1044769 |
| Reference:
|
[5] Dostálová, M., Somberg, P.: Symplectic twistor operator and its solution space on ${\mathbb{R}}^{2n}$.Complex Analysis and Operator Theory 4 (2013). MR 3144180 |
| Reference:
|
[6] Friedrich, T.: Dirac Operators in Riemannian Geometry.AMS, 2000. Zbl 0949.58032, MR 1777332 |
| Reference:
|
[7] Fulton, W., Harris, J.: Representation Theory: A First Course (Graduate Texts in Mathematics/Readings in Mathematics).Springer, 1991. MR 1153249 |
| Reference:
|
[8] Habermann, K., Habermann, L.: Introduction to symplectic Dirac operators.Lecture Notes in Mathematics, 1887, Springer-Verlag, Berlin, 2006. Zbl 1102.53032, MR 2252919 |
| Reference:
|
[9] Kadlcakova, L.: Contact Symplectic Geometry in Parabolic Invariant Theory and Symplectic Dirac Operator.Dissertation Thesis, Mathematical Institute of Charles University, Prague, 2002. Zbl 1039.58017, MR 1890440 |
| Reference:
|
[10] Kostant, B.: Symplectic Spinors.Rome Symposia XIV (1974), 139–152. Zbl 0321.58015, MR 0400304 |
| . |
