Combinatorics of the $\hat{sl}_2$ Spaces of Coinvariants

Details Combinatorics of the $\hat{sl}_2$ Spaces of Coinvariants Combinatorics of the $\hat{sl}_2$ Spaces of Coinvariants

1999-08-02

arxiv.org/abs/math-ph/9908003v4

Transformation Groups, Vol. 6, No 1 (2001), p. 25-52

Physics

Mathematical Physics

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Scientific paper

We consider two types of quotients of the integrable modules of $\hat{sl}_2$. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level-$k$. We describe monomial bases for the spaces of coinvariants, which leads to a fermionic description of these spaces. For $k=1$, we give the explicit formulas for the characters. We also present recursion relations satisfied by the characters and the monomial bases.

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