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A residue theorem for rational trigonometric sums and Verlinde's formula

Andras Szenes
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Abstract

We present a compact formula computing rational trigonometric sums. E. Verlinde's expression for the dimension of conformal blocks in WZW theory is an example of such a sum. As an application, we show that a formula of Bismut and Labourie for the Riemann-Roch numbers of moduli spaces of flat connections on a Riemann surface coincides with Verlinde's expression.

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Andras Szenes. 2001-09-06. A residue theorem for rational trigonometric sums and Verlinde's formula. https://arxiv.org/abs/math/0109038

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