The sl̂(n)k-WZNW fusion ring: A combinatorial construction and a realisation as quotient of quantum cohomology

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Abstract

A simple, combinatorial construction of the sl̂(n)k-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 Grk,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. © 2010 Elsevier Inc.

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Korff, C., & Stroppel, C. (2010). The sl̂(n)k-WZNW fusion ring: A combinatorial construction and a realisation as quotient of quantum cohomology. Advances in Mathematics, 225(1), 200–268. https://doi.org/10.1016/j.aim.2010.02.021

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