Journal of Lie Theory 17 (2007), No. 2, 427--448
Copyright Heldermann Verlag 2007
Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc
Olaf M. Schnürer
Mathematisches Institut, Universitaet Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany
olaf.schnuerer@math.uni-freiburg.de
This paper concerns regular connections on trivial algebraic G-principal fiber bundles over the infinitesimal punctured disc, where G is a connected reductive linear algebraic group over an algebraically closed field of characteristic zero. We show that the pull-back of every regular connection to an appropriate covering of the infinitesimal punctured disc is gauge equivalent to a connection of the form X z-1dz for some X in the Lie algebra of G. We may even arrange that the only rational eigenvalue of ad X is zero. Our results allow a classification of regular SLn-connections up to gauge equivalence.
Keywords: Regular connection, principal fiber bundles, infinitesimal punctured disc.
MSC: 34A99, 20G15
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