We present a compact formula computing rational trigonometric sums. Such sums appeared in the work of E. Verlinde on the dimension of conformal blocks in Wess-Zumino-Witten (WZW) theory. As an application, we show that a formula of J.-M. Bismut and F. 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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András Szenes (2003) studied this question.
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