Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Holomorphic sections of pre-quantum line bundles on

Author(s): Meng-Kiat Chuah
Journal: Proc. Amer. Math. Soc. 128 (2000), 2795-2799.
MSC (2000): Primary 22E10, 53D50
Posted: February 29, 2000
MathSciNet review: 1709745
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

Let be the Iwasawa decomposition of a complex connected semi-simple Lie group . Let $P \subset G$ be a parabolic subgroup containing , and let be its commutator subgroup. In this paper, we characterize the -invariant Kähler structures on , and study the holomorphic sections of their corresponding pre-quantum line bundles.

References:

1.: M.K. CHUAH, -invariant Kaehler structures on $K_{\mathbf{C}}/N$ and the associated line bundles, Proc. Amer. Math. Soc. 124 (1996), 3481-3491. MR 97a:32034
2.: M.K. CHUAH, The generalized Borel-Weil theorem and cohomology of , Indiana Univ. Math. J. 46 (1997), 117-131. MR 98d:22013
3.: M.K. CHUAH, Kaehler structures on $K_{\mathbf{C}}/(P,P)$ , Trans. Amer. Math. Soc. 349 (1997), 3373-3390. MR 97k:22016
4.: M.K. CHUAH, Holomorphic sections of pre-quantum line bundles on , Michigan Math. J. 45 (1998), 375-385. MR 99j:32031
5.: V. GUILLEMIN AND S. STERNBERG, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), 515-538. MR 83m:58040
6.: V. GUILLEMIN AND S. STERNBERG, Symplectic techniques in physics, Cambridge U. Press, Cambridge 1984. MR 86f:58054
7.: A. KNAPP, Representation theory of semisimple groups, Princeton U. Press, Princeton 1986. MR 87j:22022
8.: B. KOSTANT, Quantization and unitary representations, Springer Lecture Notes in Math. 170 (1970), 87-208. MR 45:3638

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22E10, 53D50

Retrieve articles in all Journals with MSC (2000): 22E10, 53D50

Additional Information:

Meng-Kiat Chuah
Affiliation: Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan
Email: chuah@math.nctu.edu.tw

DOI: 10.1090/S0002-9939-00-05636-7
PII: S 0002-9939(00)05636-7
Keywords: K\"{a}hler, Lie group, line bundle
Received by editor(s): October 15, 1998
Posted: February 29, 2000
Additional Notes: This research was supported in part by the NSC of Taiwan, Contract NSC 88-2115-M-009020
Communicated by: Roe Goodman
Copyright of article: Copyright 2000, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|