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ON HOLOMORPHIC PRINCIPAL BUNDLES OVER A COMPACT RIEMANN SURFACE ADMITTING A FLAT CONNECTION, II

Published online by Cambridge University Press:  09 June 2003

HASSAN AZAD  and
INDRANIL BISWAS
HASSAN AZAD
Affiliation:
Department of Mathematical Sciences, King Fahd University, Dhahran 31261, Saudi Arabiahassanaz@kfupm.edu.sa
INDRANIL BISWAS
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, Indiaindranil@math.tifr.res.in
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Abstract

Holomorphic principal bundles over a compact Riemann surface X that admits a flat connection are considered. A holomorphic G-bundle over X, where G is a connected semisimple linear algebraic group over ${\Bbb C}$, admits a flat connection if and only if the adjoint vector bundle admits one. More generally, for a complex reductive group G, the necessary and sufficient condition on a G-bundle to admit a flat connection is described. This simplifies the criterion obtained by the authors and given in Math. Ann. 322 (2002) 333–346.

Keywords

53C0532L05
Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 4 , July 2003 , pp. 440 - 444
Copyright
© The London Mathematical Society 2003

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