The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology
arXiv:0909.2347 · doi:10.1016/j.aim.2010.02.021
Abstract
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.
61 pages, 2 eps figures; revised version accepted for publication in Advances in Mathematics: some minor typos removed, rewording of the proof to Corollary 6.9 and figure in Example 8.3 changed
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