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

Autori
Baranović, Ivana

Izvornik
Communications in algebra (0092-7872) 39 (2011), 3; 1007-1051

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
combinatorial bases; affine Lie algebras

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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