The equivariant Verlinde formula on the moduli of Higgs bundles

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.

arXiv comment22 pages, Appendix by Constantin Teleman, new version corrects a typo in the abstract

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Cited by in corpus (11)

• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• The Verlinde formula for Higgs bundles
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• Verlinde formulae on complex surfaces: K-theoretic invariants
• 3d N=2 Chern-Simons-matter theory, Bethe ansatz, and quantum K-theory of Grassmannians
• Twisted argyle quivers and Higgs bundles
• Mirror symmetry with branes by equivariant Verlinde formulae
• Sheaves on surfaces and virtual invariants
• Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups
• Theta-stratifications, Theta-reductive stacks, and applications
• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories