Polynomial relations for \(q\)-characters via the ODE/IM correspondence

DOI10.3842/SIGMA.2012.028zbMath1247.81219arXiv1201.1614MaRDI QIDQ431486

Juanjuan Sun

Publication date: 26 June 2012

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.1614

zbMATH Keywords

\(q\)-characterBorel subalgebraBaxter's \(Q\)-operatorODE/IM correspondence

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Yang-Baxter equations (16T25)

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WKB periods for higher order ODE and TBA equations ⋮ Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case ⋮ Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers ⋮ WKB analysis of the linear problem for modified affine Toda field equations ⋮ Baxter's relations and spectra of quantum integrable models ⋮ ODE/IM correspondence and the Argyres-Douglas theory ⋮ Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case ⋮ ODE/IM correspondence for modified \(B_2^{(1)}\) affine Toda field equation ⋮ Counting monster potentials ⋮ ODE/IM correspondence and modified affine Toda field equations ⋮ Opers for higher states of quantum KdV models ⋮ Massive ODE/IM correspondence and nonlinear integral equations for ${A_r^{(1)}}$ -type modified affine Toda field equations ⋮ ODE/IM correspondence and supersymmetric affine Toda field equations ⋮ TBA equations for the Schrödinger equation with a regular singularity ⋮ ODE/IM correspondence for affine Lie algebras: a numerical approach

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