Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc

Details Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc

2006-10-09

arxiv.org/abs/math/0610250v1

Mathematics

Representation Theory

20 pages

Scientific paper

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^{-1}dz 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 SL_n-connections up to gauge equivalence.

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