Residue Theorem for Rational Trigonometric Sums and Verlinde’s Formula
نویسنده
چکیده
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 WessZumino-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.
منابع مشابه
A Residue Theorem for Rational Trigonometric Sums and Verlinde’s Formula
where k is a fixed positive integer. The interest in such sums was motivated by a beautiful formula of E. Verlinde for the dimension of the “space of conformal blocks” in the WZW theory [18]. The data for Verlinde’s formula is a simple simply-connected Lie group G, non-negative integers g and k, and, in the simplest case of one puncture, a dominant highest weight λ of G satisfying certain condi...
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