Glasnik Matematicki, Vol. 52, No. 1 (2017), 53-77.

TWISTED SL(3, C)˜-MODULES AND COMBINATORIAL IDENTITIES

Ivica Siladić

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 A₂⁽²⁾. This description also gives two new combinatorial identities of Göllnitz (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.

2010 Mathematics Subject Classification.   17B67, 05A19.

Key words and phrases.   Twisted affine Lie algebras, standard modules, vertex operator algebras, colored partitions, Rogers-Ramanujan identities.

DOI: 10.3336/gm.52.1.05

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