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Journal of Lie Theory 17 (2007), No. 1, 145--161
Copyright Heldermann Verlag 2007

Infinite Fusion Products and sl2 Cosets

Evgeny Feigin
Independent University, Bolshoy Vlasievsky 11, 119002 Moscow, Russia


We study an approximation of tensor product of irreducible integrable $\widehat{{\frak{sl}}_2}$ 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 $\widehat{{\frak{sl}}_2}$ branching functions.

Keywords: Cosets, branching functions, Kostka polynomials.

MSC: 17B67, 81R10

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