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The Verlinde formula for Higgs bundles
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abstract
We propose and prove the Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. This generalizes the equivariant Verlinde formula for the case of $SU(n)$ proposed previously by the second and third author. We further establish a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks. Finally, we prove that these dimensions form a one-parameter family of $1+1$-dimensional TQFT, uniquely classified by the complex Verlinde algebra, which is a one-parameter family of Frobenius algebras. We construct this one-parameter family of Frobenius algebras as a deformation of the classical Verlinde algebra for $G$.
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A universal Higgs bundle moduli space
A symplectic connection over Teichmüller space, derived from the harmonic-map energy, carries an integrable complex structure that realizes the universal Higgs bundle moduli space and satisfies Higgs-bundle-like curva...
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