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

B. Feigin·R. Kedem·S. Loktev·T. Miwa·E. Mukhin
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Abstract

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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B. Feigin, R. Kedem, S. Loktev, T. Miwa, E. Mukhin. 2001-03-19. Combinatorics of the $\hat{sl}_2$ Spaces of Coinvariants. https://arxiv.org/abs/math-ph/9908003

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