Polynomial Relations for q-Characters via the ODE/IM Correspondence

TL;DR

This paper explores polynomial relations among q-characters of representations of quantum affine algebra's Borel subalgebra, inspired by the ODE/IM correspondence, proposing conjectural relations in this mathematical framework.

Contribution

It introduces conjectural polynomial relations among q-characters of certain representations, connecting quantum affine algebras with the ODE/IM correspondence.

Findings

Proposes conjectural polynomial relations among q-characters.

Links quantum affine algebra representations with integrable models.

Provides a new perspective on the structure of q-characters.

Abstract

Let $U_q(\mathfrak{b})$ be the Borel subalgebra of a quantum affine algebra of type $X^{(1)}_n$ ($X=A,B,C,D$). Guided by the ODE/IM correspondence in quantum integrable models, we propose conjectural polynomial relations among the $q$-characters of certain representations of $U_q(\mathfrak{b})$.