Twisted $\mathfrak{s}\mathfrak{l}(3,\text{C})\text{sptilde}$-modules and combinatorial identities

The main result of this paper is a combinatorial description of a basis of standard level 1 module for the twisted affine Lie algebra $A_2^{(2)}\mathrm{.}$ This description also gives two new combinatorial identities of G"ollnitz (or Rogers–Ramanujan) type. Methods used through the paper are mainly developed by J. Lepowsky, R. L. Wilson, A. Meurman and M. Primc, and the crucial role in constructions plays a vertex operator algebra approach to standard representations of affine Lie algebras.