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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

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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