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)

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, Professor 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