2015/11/30 by Davide Masoero, Andrea Raimondo, Daniele Valeri
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Bethe ansatz #Connection (principal bundle) #Integrable system #Korteweg–de Vries equation #Lie algebra #Lie conformal algebra #Mathematical analysis #Mathematics #Meromorphic function #Nonlinear Waves and Solitons #Nonlinear system #Ode #Physics #Pure mathematics #Quantum mechanics #hep-th #math-ph #math.MP #math.QA #msc:17B67 #msc:34M40 #msc:37K30 #msc:82B23
paper · pdf · doi:10.1007/s00220-016-2744-2
published as Commun. Math. Phys. (2017) 349: 1063 · 37 pages, 1 figure. Continuation of arXiv:1501.07421. Minor change in the title. New subsection 5.1 on the action of the Weyl group on the Bethe Ansatz solutions
arxiv created 2016/06/16 · openalex publication_date 2016/09/17 · arxiv updated 2017/02/17 · openalex created_date 2020/10/01 · openalex updated_date 2026/08/05
We assess the ODE/IM correspondence for the quantum \mathfrakg-KdV model, for a non-simply laced Lie algebra \mathfrakg. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra \mathfrakg(1), and constructing the relevant Ψ-system among subdominant solutions. We then use the Ψ-system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum \mathfrakg-KdV model. We also consider generalized Airy functions for twisted Kac--Moody algebras and we construct new explicit solutions to the Bethe Ansatz equations. The paper is a continuation of our previous work on the ODE/IM correspondence for simply-laced Lie algebras.