Journal of Lie Theory EMIS ELibM Electronic Journals 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 groups

Andreas Kriegl, Mark Losik, and Peter W. Michor

A.\ Kriegl
Institut für Mathematik
Universität Wien
Strudlhofgasse 4, A-1090 Wien
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
M. Losik
Saratov State University
ul. Astrakhanskaya, 83
410026 Saratov, Russia

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.

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Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.

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