book chapter published yes Tamás Hausel author 4A0666D8-F248-11E8-B48F-1D18A9856A870000-0002-9582-2634 Anton Mellit author 388D3134-F248-11E8-B48F-1D18A9856A87 Du Pei author TaHa department 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. Oxford University Press2018 eng 978019880201310.1093/oso/9780198802013.003.0009 189-218 T. Hausel, A. Mellit, D. Pei, in:, Geometry and Physics: Volume I, Oxford University Press, 2018, pp. 189–218. Hausel T, Mellit A, Pei D. Mirror symmetry with branes by equivariant verlinde formulas. In: <i>Geometry and Physics: Volume I</i>. Oxford University Press; 2018:189-218. doi:<a href="https://doi.org/10.1093/oso/9780198802013.003.0009">10.1093/oso/9780198802013.003.0009</a> T. Hausel, A. Mellit, and D. Pei, “Mirror symmetry with branes by equivariant verlinde formulas,” in <i>Geometry and Physics: Volume I</i>, Oxford University Press, 2018, pp. 189–218. Hausel, Tamás, Anton Mellit, and Du Pei. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” In <i>Geometry and Physics: Volume I</i>, 189–218. Oxford University Press, 2018. <a href="https://doi.org/10.1093/oso/9780198802013.003.0009">https://doi.org/10.1093/oso/9780198802013.003.0009</a>. Hausel, T., Mellit, A., &#38; Pei, D. (2018). Mirror symmetry with branes by equivariant verlinde formulas. In <i>Geometry and Physics: Volume I</i> (pp. 189–218). Oxford University Press. <a href="https://doi.org/10.1093/oso/9780198802013.003.0009">https://doi.org/10.1093/oso/9780198802013.003.0009</a> Hausel T, Mellit A, Pei D. 2018.Mirror symmetry with branes by equivariant verlinde formulas. In: Geometry and Physics: Volume I. , 189–218. Hausel, Tamás, et al. “Mirror Symmetry with Branes by Equivariant Verlinde Formulas.” <i>Geometry and Physics: Volume I</i>, Oxford University Press, 2018, pp. 189–218, doi:<a href="https://doi.org/10.1093/oso/9780198802013.003.0009">10.1093/oso/9780198802013.003.0009</a>. 65252019-06-06T12:42:01Z2026-04-16T10:30:22Z