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