Glasnik Matematicki, Vol. 47, No. 1 (2012), 133-142.

THE GENERATING CONDITION FOR THE EXTENSION OF THE CLASSICAL GAUSS SERIES-PRODUCT IDENTITY

Tomislav Šikić

Abstract.   In this paper a condition is presented on parameters (n₁,n₂,Λ_k), for arbitrary partition n={n₁, n₂}, (n₁≤ n₂) and k=1,...,n-1, which guarantees that two different interpretations of characters of fundamental modules L(Λ_k) for the affine Kac-Moody Lie algebra generate extended classical Gauss series-product identities.

2010 Mathematics Subject Classification.   17B67.

Key words and phrases.   Affine Lie algebras, characters of fundamental modules, series-product identities, classical Gauss identity.

DOI: 10.3336/gm.47.1.10

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