Tensor fields and connections on holomorphic orbit spaces of finite groups

2002/03/31 by Andreas Kriegl, Mark Losik, Peter W. Michor
Mathematics · #math.DG #math.CV #math.RT #msc:32M17

paper · pdf

published as J. Lie Theory 13 (2003), 519--534 · 15 pages, LaTeX, some arguments rearranged

arxiv created 2002/10/29 · arxiv updated 2009/11/30

Abstract

For a representation of a finite group G on a complex vector space V we determine when a holomorphic \binompq-tensor field on the principle 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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