Residue theorem for rational trigonometric sums and Verlinde's formula

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Residue theorem for rational trigonometric sums and Verlinde's formula

András Szenes

Source: Duke Math. J. Volume 118, Number 2 (2003), 189-227.

Abstract

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.

Primary Subjects: 11L03

Secondary Subjects: 14H60, 14N20

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1082744646
Mathematical Reviews number (MathSciNet): MR1980993
Digital Object Identifier: doi:10.1215/S0012-7094-03-11821-9
Zentralblatt MATH identifier: 1042.14030

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