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

TL;DR

This paper provides a combinatorial basis for a level 1 module of a twisted affine Lie algebra and derives two new identities of Rogers-Ramanujan type using vertex operator algebra methods.

Contribution

It introduces a new combinatorial description of the basis for twisted affine Lie algebra modules and establishes two novel identities of Rogers-Ramanujan type.

Findings

New combinatorial basis for twisted affine Lie algebra modules

Two new Rogers-Ramanujan type identities

Application of vertex operator algebra methods

Abstract

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.