The combinatorics of the Verlinde formulas

TL;DR

This paper presents a residue formula for the Verlinde formula, enabling polynomial computation of its coefficients in relation to the level and linking it to the Riemann-Roch theorem on moduli spaces.

Contribution

It introduces a residue-based approach to compute Verlinde coefficients, connecting algebraic and geometric perspectives in the theory.

Findings

Residue formula for Verlinde coefficients

Polynomial expression in level for coefficients

Connection to Riemann-Roch on moduli space

Abstract

A residue formula is given for the Verlinde formula, which allows one to calculate its coefficients as a polynomial in the level and connects it to the Riemann-Roch formula on the moduli space of vector bundles on a curve.