
TL;DR
This paper establishes identities between different polynomial families related to affine algebra characters, connecting combinatorial sums with Bethe-Ansatz solutions, and proposes a new fermionic sum representation.
Contribution
It proves identities among polynomial families linked to affine $su(2)$ characters and introduces a novel fermionic sum derived from Bethe-Ansatz solutions.
Findings
Identities between bosonic, fermionic, and configuration sum polynomials.
Different expressions for affine $su(2)$ characters at level one.
A conjectured fermionic sum representation from Bethe-Ansatz.
Abstract
We prove an identity between three infinite families of polynomials which are defined in terms of `bosonic', `fermionic', and `one-dimensional configuration' sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-Ansatz solution of the Heisenberg spin chain.
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