Geodesic
Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc
Olaf M. Schnürer1
1Mathematisches Institut, Universitaet Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany
Journal of Lie Theory, Tome 17 (2007) no. 2, pp. 427-448

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 34A99, 20G15
Mots-clés : Regular connection, principal fiber bundles, infinitesimal punctured disc

Olaf M. Schnürer  1

1 Mathematisches Institut, Universitaet Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany 
Olaf M. Schnürer. Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc. Journal of Lie Theory, Tome 17 (2007) no. 2, pp. 427-448. http://geodesic.mathdoc.fr/item/JOLT_2007_17_2_a10/
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     title = {Regular {Connections} on {Principal} {Fiber} {Bundles} over the {Infinitesimal} {Punctured} {Disc}},
     journal = {Journal of Lie Theory},
     pages = {427--448},
     year = {2007},
     volume = {17},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_2_a10/}
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