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

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

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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.

Item Type:Articles (Other)
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Korff, Dr Christian and Stroppel, Dr Catharina
Authors: Korff, C., and Stroppel, C.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Journal Abbr.:Adv. Math.
ISSN:0001-8708
ISSN (Online):1090-2082
Published Online:19 March 2010

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