The authors prove, via an embedding into C_2^(1) and an intertwining operator, that the combinatorial monomial basis of every standard A_1^(1) module is linearly independent.
Combinatorics of the $\hat{sl}_2$ Spaces of Coinvariants
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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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Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$
The authors prove, via an embedding into C_2^(1) and an intertwining operator, that the combinatorial monomial basis of every standard A_1^(1) module is linearly independent.