Title:
|
Symplectic spinor valued forms and invariant operators acting between them (English) |
Author:
|
Krýsl, Svatopluk |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
|
1212-5059 (online) |
Volume:
|
42 |
Issue:
|
5 |
Year:
|
2006 |
Pages:
|
279-290 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described. (English) |
MSC:
|
53C27 |
MSC:
|
53D05 |
MSC:
|
58J60 |
idZBL:
|
Zbl 1164.58320 |
idMR:
|
MR2322414 |
. |
Date available:
|
2008-06-06T22:49:46Z |
Last updated:
|
2012-05-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108034 |
. |
Reference:
|
[1] Baldoni W.: General Representation theory of real reductive Lie groups in Bailey, T. N.: Representation Theory and Automorphic Forms.Edinburgh (1996), 61–72. MR 1476492 |
Reference:
|
[2] Britten D. J., Hooper J., Lemire F. W.: Simple $C_n$-modules with multiplicities 1 and application.Canad. J. Phys. 72 (1994), 326–335. MR 1297597 |
Reference:
|
[3] Britten D. J., Lemire F. W.: On modules of bounded multiplicities for the symplectic algebra.Trans. Amer. Math. Soc. 351, No. 8 (1999), 3413–3431. MR 1615943 |
Reference:
|
[4] Delanghe R., Sommen F., Souèek V.: Clifford Algebra and Spinor-valued Functions.Math. Appl., Vol. 53, 1992. |
Reference:
|
[5] Goodman R., Wallach N.: Representations and Invariants of the Classical Groups.Cambridge University Press, Cambridge, 2003. Zbl 1173.22001 |
Reference:
|
[6] Green M. B., Hull C. M.: Covariant quantum mechanics of the superstring.Phys. Lett. B 225 (1989), 57–65. MR 1006387 |
Reference:
|
[7] Habermann K.: Symplectic Dirac Operators on Kähler Manifolds.Math. Nachr. 211 (2000), 37–62. MR 1743488 |
Reference:
|
[8] Humphreys J. E.: Finite and infinite dimensional modules for semisimple Lie algebras, Lie theories and their applications.Lie Theor. Appl., Proc. Ann. Semin. Can. Math. Congr., Kingston 1977 (1978), 1–64. MR 0500456 |
Reference:
|
[9] Kac V. G., Wakimoto M.: Modular invariant representations of infinite dimensional Lie algebras and superalgebras.Proc. Natl. Acad. Sci. USA 85, No. 14 (1988), 4956–4960. Zbl 0652.17010, MR 0949675 |
Reference:
|
[10] Kadlčáková L.: Dirac operator in parabolic contact symplectic geometry.Ph.D. thesis, Charles University Prague, Prague, 2001. |
Reference:
|
[11] Kashiwara M., Vergne M.: On the Segal-Shale-Weil representation and harmonic polynomials.Invent. Math. 44, No. 1 (1978), 1–49. MR 0463359 |
Reference:
|
[12] Klein A.: Eine Fouriertransformation für symplektische Spinoren und Anwendungen in der Quantisierung.Diploma Thesis, Technische Universität Berlin, Berlin, 2000. |
Reference:
|
[13] Kostant B.: On the Tensor Product of a Finite and an Infinite Dimensional Representations.J. Funct. Anal. 20 (1975), 257–285. MR 0414796 |
Reference:
|
[14] Kostant B.: Symplectic Spinors.Sympos. Math. XIV (1974), 139–152. Zbl 0321.58015, MR 0400304 |
Reference:
|
[15] Krýsl S.: Invariant differential operators for contact projective geometries.Ph.D. thesis, Charles University Prague, Prague, 2004. |
Reference:
|
[16] Krýsl S.: Decomposition of the tensor product of the defining representation and a higher symplectic spinor module over $\mathfrak{sp}(2n,\mathbb{C})$.to appear in J. Lie Theory 17, No. 1 (2007), 63–72. MR 2286881 |
Reference:
|
[17] Reuter M.: Symplectic Dirac-Kähler Fields.J. Math. Phys. 40 (1999), 5593–5640; electronically available at hep-th/9910085. Zbl 0968.81037, MR 1722329 |
. |