Journal of Lie TheoryVol. 13, No. 2, pp. 519--534 (2003)
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Journal of Lie Theory Vol. 13, No. 2, pp. 519--534 (2003) |
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Tensor fields and connections on holomorphic orbit spaces of finite groupsAndreas Kriegl, Mark Losik, and Peter W. MichorA.\ KrieglInstitut für Mathematik Universität Wien Strudlhofgasse 4, A-1090 Wien Austria Andreas.Kriegl@univie.ac.at, P.\ W.\ Michor Institut für Mathematik Universität Wien Strudlhofgasse 4, A-1090 Wien Austria and Erwin Schrödinger Institut für Mathematische Physik Boltzmanngasse 9, A-1090 Wien Austria Peter.Michor@esi.ac.at, and M. Losik Saratov State University ul. Astrakhanskaya, 83 410026 Saratov, Russia LosikMV@info.sgu.ru Abstract: For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic ${p\choose q}$-tensor field on the principal stratum of the orbit space $V/G$ can be lifted to a holomorphic $G$-invariant tensor field on $V$. This extends also to connections. As a consequence we determine those holomorphic diffeomorphisms on $V/G$ which can be lifted to orbit preserving holomorphic diffeomorphisms on $V$. This in turn is applied to characterize complex orbifolds. Full text of the article:
Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.
© 2003 Heldermann Verlag
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