Infinite fusion products and $\hat{\mathfrak{sl}_2}$ cosets

Details Infinite fusion products and $\hat{\mathfrak{sl}_2}$ cosets Infinite fusion products and $\hat{\mathfrak{sl}_2}$ cosets

2006-03-09

arxiv.org/abs/math/0603226v1

Mathematics

Quantum Algebra

17 pages

Scientific paper

In this paper we study an approximation of tensor product of irreducible integrable $\hat{\mathfrak{sl}_2}$ representations by infinite fusion products. This gives an approximation of the corresponding coset theories. As an application we represent characters of spaces of these theories as limits of certain restricted Kostka polynomials. This leads to the bosonic (which is known) and fermionic (which is new) formulas for the $\hat{\mathfrak{sl}_2}$ branching functions.

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