The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology

Understand

A simple, combinatorial construction of the sl(n)-WZNW fusion ring, also known as Verlinde algebra, is given.

• As a byproduct of the construction one obtains an isomorphism between the fusion ring and a particular quotient of the small quantum cohomology ring of the Grassmannian Gr(k,k+n).
• We explain how our approach naturally fits into known combinatorial descriptions of the quantum cohomology ring, by establishing what one could call a `Boson-Fermion-correspondence' between the two rings.
• We also present new recursion formulae for the structure constants of both rings, the fusion coefficients and the Gromov-Witten invariants.