Communications in Mathematical Physics

, Volume 349, Issue 3, pp 1063–1105 | Cite as

Bethe Ansatz and the Spectral Theory of Affine Lie algebra–Valued Connections II: The Non Simply–Laced Case

Article

Abstract

We assess the ODE/IM correspondence for the quantum \({\mathfrak{g}}\)-KdV model, for a non-simply laced Lie algebra \({\mathfrak{g}}\). This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra \({{\mathfrak{g}}^{(1)}}\), and constructing the relevant \({\Psi}\)-system among subdominant solutions. We then use the \({\Psi}\)-system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum \({\mathfrak{g}}\)-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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Davide Masoero
    • 1
  • Andrea Raimondo
    • 1
    • 2
  • Daniele Valeri
    • 3
  1. 1.Grupo de Física Matemática da Universidade de LisboaLisbonPortugal
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di Milano-BicoccaMilanItaly
  3. 3.Yau Mathematical Sciences CenterTsinghua UniversityBeijingChina

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