Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 2 standard modules for $D_4^{(1)}$
Abstract
Description
Let $\gtl$ be an affine Lie algebra of type $D_{\ell}^{(1)}$ and $L(Λ)$ its standard module with a highest weight vector $v_Λ$. For a given $\Z$-gradation $\gtl = \gtl_{-1} + \gtl_0 + \gtl_1$, we define Feigin-Stoyanovsky's type subspace as $$W(Λ) = U(\gtl_1) \cdot v_Λ.$$ By using vertex operator relations for standard modules we reduce the Ponicaré-Brikhoff-Witt spanning set of $W(Λ)$ to a basis and prove its linear independence by using Dong-Lepowsky intertwining operators.