An Extension of the Classical Gauss Series-product Identity by Fermionic Construction of \hat{sl}_n

TL;DR

This paper introduces two infinite classes of series-product identities derived from classical Gauss identities and affine Lie algebra character formulas, expanding the mathematical understanding of these identities.

Contribution

It presents novel series-product identities based on affine Lie algebra characters, extending classical Gauss identities with a fermionic construction approach.

Findings

Two new classes of series-product identities are established.

The identities are connected to affine Lie algebra representations.

The work provides a new perspective on classical identities through algebraic structures.

Abstract

The main result of this paper is two infinity classes of series-product identities which is based on classical Gauss identity and two different interpretations of character formula for irreducible highest weight modules of affine Lie algebras.