Journal of Lie Theory

no. 2
Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc
Journal of Lie Theory, Volume 17 (2007) no. 2, pp. 427-448
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.
DOI: 10.5802/jolt.454
Classification: 34A99, 20G15
Keywords: Regular connection, principal fiber bundles, infinitesimal punctured disc 
@article{JOLT_2007_17_2_a10,
     author = {O. M. Schn\"urer},
     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},
     doi = {10.5802/jolt.454},
     zbl = {1122.53014},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.454/}
}
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O. M. Schnürer. Regular Connections on Principal Fiber Bundles over the Infinitesimal Punctured Disc. Journal of Lie Theory, Volume 17 (2007) no. 2, pp. 427-448. doi: 10.5802/jolt.454

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