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.
Bases of Feigin-Stoyanovsky's type subspaces for $C_\ell^{(1)}$
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abstract
In this paper we construct combinatorial bases of Feigin-Stoyanovsky's type subspaces of standard modules for level $k$ affine Lie algebra $C_\ell^{(1)}$. We prove spanning by using annihilating field $x_\theta (z)^{k+1}$ of standard modules. In the proof of linear independence we use simple currents and intertwinining operators whose existence is given by fusion rules.
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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.