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Geometry and Physics: Volume IA Festschrift in honour of Nigel Hitchin$
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Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada

Print publication date: 2018

Print ISBN-13: 9780198802013

Published to Oxford Scholarship Online: December 2018

DOI: 10.1093/oso/9780198802013.001.0001

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Mirror Symmetry with Branes by Equivariant Verlinde Formulas

Mirror Symmetry with Branes by Equivariant Verlinde Formulas

Chapter:
(p.189) 9 Mirror Symmetry with Branes by Equivariant Verlinde Formulas
Source:
Geometry and Physics: Volume I
Author(s):

Tamás Hausel

Anton Mellit

Du Pei

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198802013.003.0009

This chapter finds an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL2 Higgs moduli space on a Riemann surface. On one side of the agreement, components of the Lagrangian brane of U(1,1) Higgs bundles, whose mirror was proposed by Hitchin to be certain even exterior powers of the hyperholomorphic Dirac bundle on the SL2 Higgs moduli space, are present. The agreement arises from a mysterious functional equation. This gives strong computational evidence for Hitchin’s proposal.

Keywords:   mirror symmetry, Higgs bundle, brane, Verlinde formula, Lagrangian brane

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