Holomorphic principal bundles over elliptic curves

Abstract

In this paper, the first of a series of three, we classify holomorphic principal G-bundles over an elliptic curve, where G is a reductive group. We also study the local and global properties of the moduli space of semistable G-bundles. We identify canonical representatives for each S-equivalence class of semistable G-bundles, and study their automorphism groups.

68 pages, AMS-TeX, amsppt style

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• Moduli space of $G$-connections on an elliptic curve
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• An O(2,n) formulation of invariant theory for elliptic Weyl group
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