, 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.

Dedicated to the memory of Denis Uglov
Supported by NSF grant number 9870550.
Partially supported by CRDF grant RM1-265.