, Volume 6, Issue 1, pp 25-52

Combinatorics of the\(\widehat{\mathfrak{s}\mathfrak{l}}_2 \) spaces of coinvariants

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We consider two types of quotients of the integrable modules of\(\widehat{\mathfrak{s}\mathfrak{l}}_2 \). These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of levelk. We describe monomial bases for the spaces of coinvariants, which leads to a fermionic description of these spaces. Fork=1, we give explicit formulas for the characters. We also present recursion relations satisfied by the characters and the monomial bases.