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arXiv · 0812.3684

Loop groups and holomorphic bundles

Jacques C. Hurtubise·Michael K. Murray
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Abstract

This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of G-bundles with additional flag structure along a line is proven for any reductive group; this gives the corresponding stability statement for any compact group K for the moduli of K-instantons over the four-sphere, and for the moduli of K-calorons over the three-sphere times the circle. The paper also considers the Hecke transforms on bundles induced by outer automorphisms of the loop groups.

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Jacques C. Hurtubise, Michael K. Murray. 2008-12-18. Loop groups and holomorphic bundles. https://arxiv.org/abs/0812.3684

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