A residue theorem for rational trigonometric sums and Verlinde's formula
Andras Szenes
TL;DR
This paper introduces a compact formula for rational trigonometric sums, exemplified by Verlinde's formula for conformal blocks, and demonstrates its application in relating Riemann-Roch numbers to these sums.
Contribution
It provides a new unified formula for rational trigonometric sums and connects Verlinde's formula with Riemann-Roch numbers of moduli spaces.
Findings
Verlinde's formula is a special case of the new sum formula
The new formula simplifies computation of conformal blocks
Riemann-Roch numbers coincide with Verlinde's expression via the new formula
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Advanced Algebra and Geometry