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

Details Twisted ${\mathfrak{sl}}(3,\C)\sptilde$-modules and combinatorial identities Twisted ${\mathfrak{sl}}(3,\C)\sptilde$-modules and combinatorial identities

2002-04-03

arxiv.org/abs/math/0204042v2

Mathematics

Quantum Algebra

28 pages, AMSTeX

Scientific paper

The main result of this paper is a combinatorial description of a basis of standard level 1 module for the twisted affine Lie algebra $A_2^{(2)}.$ 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.

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