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arXiv · 1608.01754

The equivariant Verlinde formula on the moduli of Higgs bundles

Daniel Halpern-Leistner
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Abstract

We prove an analog of the Verlinde formula on the moduli space of semistable meromorphic G-Higgs bundles over a smooth curve for a reductive group G whose fundamental group is free. The formula expresses the graded dimension of the space of sections of a positive line bundle as a finite sum whose terms are indexed by formal solutions of a generalized Bethe ansatz equation on the maximal torus of G. In an appendix, Constantin Teleman proves a vanishing theorem for the higher cohomology of positive line bundles on the stack of Higgs bundles.

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Daniel Halpern-Leistner. 2016-08-05. The equivariant Verlinde formula on the moduli of Higgs bundles. https://arxiv.org/abs/1608.01754

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