engleski

The generating condition for the extension of the classical Gauss series-product identity

In this paper a condition is presented on the parameters $(n_1, n_2, \Lambda_k)$, for arbitrary partition $\underline{; ; ; ; ; n}; ; ; ; ; =\{; ; ; ; ; n_1, n_2) (n_1\leq n_2)\}; ; ; ; ; $ and $k=1, ..., n-1$, which guarantees that two different interpretations of the characters of the fundamental modules $L(\Lambda_k)$ for the affine Lie algebra $\hat\mathfrak sl_n$ generate extended classical Gauss series-product identities.

Affine Lie algebras ; characters of fundamental modules ; series-product identities ; classical Gauss identity

AMS subject classifications: 17B67