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

Abstract

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

References in corpus (6)

• The ODE/IM Correspondence
• Baxter Q-Operators and Representations of Yangians
• Baxter's Q-operators for supersymmetric spin chains
• Asymptotic representations and Drinfeld rational fractions
• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• The Baxter's Q-operator for the W-algebra $W_N$

Cited by in corpus (12)

• Baxter's Relations and Spectra of Quantum Integrable Models
• Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case
• Bethe Ansatz and the Spectral Theory of affine Lie algebra--valued connections II. The non simply--laced case
• ODE/IM correspondence and modified affine Toda field equations
• TBA equations for the Schrödinger equation with a regular singularity
• ODE/IM correspondence and Bethe ansatz for affine Toda field equations
• WKB periods for higher order ODE and TBA equations
• ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation
• ODE/IM correspondence for affine Lie algebras: A numerical approach
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• Integrals of motion in conformal field theory with W-symmetry and the ODE/IM correspondence