A proof of polynomial identities of type $\widehat{sl(n)_1} \otimes \widehat{sl(n)_1} / \widehat{sl(n)_2}$

TL;DR

This paper proves polynomial identities for finite analogues of branching functions associated with a specific affine Lie algebra coset, advancing understanding in algebraic combinatorics and representation theory.

Contribution

It provides a rigorous proof of polynomial identities for finite analogues of branching functions in a particular affine Lie algebra coset, which was previously unproven.

Findings

Established polynomial identities for finite analogues of branching functions.

Connected algebraic identities with affine Lie algebra coset structures.

Enhanced mathematical understanding of representation theory related to $ ext{sl}(n)$.

Abstract

We present a proof of polynomial identities related to finite analogues of the branching functions of the coset $\widehat{sl(n)_1} \otimes \widehat{sl(n)_1} / \widehat{sl(n)_2}$.