engleski

Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 2 standard modules for $D_4^{; ; ; ; (1)}; ; ; ; $

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

combinatorial bases; affine Lie algebras

nije evidentirano