20.03.2012 (Tuesday)

A q-deformed Verlinde algebra

Regular Seminar Christian Korff (Glasgow)

16:00 City U.
room CG04

We generalise a recent combinatorial description of the Verlinde or WZW fusion algebra of type A by defining cylindric Macdonald functions. The latter arise as weighted sums over non-intersecting paths on a square lattice with periodic boundary conditions. Expanding the cylindric Macdonald functions into Schur functions one obtains generalised Kostka-Foulkes polynomials. The latter contain ordinary Kostka-Foulkes polynomials, which appear in algebraic geometry, representation theory and combinatorics, as special case. We further motivate the cylindric Schur functions by showing that they are connected with a commutative Frobenius algebra which can be interpreted as a deformation of the Verlinde algebra: its structure constants are polynomials whose constant terms are the WZW fusion coefficients.