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Combinatorial bases of modules for affine Lie algebra B_2^(1)
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abstract
In this paper we construct bases of standard (i.e. integrable highest weight) modules $L(\Lambda)$ for affine Lie algebra of type $B_2\sp{(1)}$ consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces $W(\Lambda)$ of $L(\Lambda)$ by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence $W(k\Lambda_0)$ for $B_2\sp{(1)}$ and the integrable highest weight module $L(k\Lambda_0)$ for $A_1\sp{(1)}$ have the same parametrization of combinatorial bases and the same presentation $\mathcal P/\mathcal I$\,.
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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.
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