Previous |  Up |  Next

Article

Title: Yamabe operator via BGG sequences (English)
Author: Tuček, Vít
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 48
Issue: 5
Year: 2012
Pages: 411-422
Summary lang: English
.
Category: math
.
Summary: We show that the conformally invariant Yamabe operator on a complex conformal manifold can be constructed as a first BGG operator by inducing from certain infinite-dimensional representation. (English)
Keyword: Bernstein-Gelfand-Gelfand resolution
Keyword: Cartan connection
Keyword: parabolic geometry
Keyword: Yamabe operator
MSC: 53A30
MSC: 53A55
MSC: 58J10
idMR: MR3007622
DOI: 10.5817/AM2012-5-411
.
Date available: 2012-12-17T14:05:45Z
Last updated: 2013-09-19
Stable URL: http://hdl.handle.net/10338.dmlcz/143115
.
Reference: [1] Calderbank, D. M. J., Diemer, T.: Differential invariants and curved Bernstein–Gelfand–Gelfand sequences.J. Reine Angew. Math. 537 (2001), 67–103. Zbl 0985.58002, MR 1856258
Reference: [2] Cap, A., Gover, A. R, Hammerl, M.: Projective BGG equations, algebraic sets, and compactifications of Einstein geometries.arXiv:1005.2246, May 2010.
Reference: [3] Čap, A., Slovák, J.: Parabolic geometries. I.Math. Surveys Monogr., American Mathematical Society, 2009. Zbl 1183.53002, MR 2532439
Reference: [4] Čap, A., Slovák, J., Souček, V.: Bernstein–Gelfand–Gelfand Sequences.Ann. of Math. (2) 154 (1) (2001), 97–113. Zbl 1159.58309, MR 1847589, 10.2307/3062111
Reference: [5] Davidson, M. G., Enright, T. J., Stanke, R. J.: Differential operators and highest weight representations.Mem. Amer. Math. Soc. 94 (455) (1991), iv+102. Zbl 0759.22015, MR 1081660
Reference: [6] Enright, T., Howe, R., Wallach, N.: A classification of unitary highest weight modules.Representation theory of reductive groups (Park City, Utah, 1982), Birkhäuser Boston, 1983. Zbl 0535.22012, MR 0733809
Reference: [7] Enright, T. J.: Analogues of Kostant’s $\mathfrak{u}$–cohomology formulas for unitary highest weight modules.392 (1988), 27–36. MR 0965055
Reference: [8] Gover, A. R., Hirachi, K.: Conformally invariant powers of the Laplacian – A complete nonexistence theorem.J. Amer. Math. Soc. 17 (2004), 389–405. Zbl 1066.53037, MR 2051616, 10.1090/S0894-0347-04-00450-3
Reference: [9] Graham, C. R.: Conformally invariant powers of the Laplacian. II. Nonexistence.J. London Math. Soc. (2) 46 (3) (1992), 566–576. Zbl 0726.53011, MR 1190439, 10.1112/jlms/s2-46.3.566
Reference: [10] Huang, Jing–Song, Pandžič, P., Renard, D.: Dirac operators and Lie algebra cohomology.Represent. Theory 10 (2006), 299–313. Zbl 1134.22011, MR 2240703, 10.1090/S1088-4165-06-00267-6
Reference: [11] Kostant, B.: Lie algebra cohomology and the generalized Borel–Weil Theorem.Ann. of Math. (2) 74 (1961), 329–387. Zbl 0134.03501, MR 0142696, 10.2307/1970237
Reference: [12] Pandžič, P.: Dirac operators on Weil representations II.Math. Commun. 15 (2) (2010), 411–424. Zbl 1207.22009, MR 2814264
Reference: [13] Vogan, D. A., Jr., : Unitary representations and complex analysis.Representation theory and complex analysis, Lecture Notes in Math., vol. 1931, Springer, Berlin, 2008, pp. 259–344. Zbl 1143.22002, MR 2409701
.

Files

Files Size Format View
ArchMathRetro_048-2012-5_10.pdf 458.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo