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

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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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Correspondence to Davide Masoero.

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Communicated by Y. Kawahigashi

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Masoero, D., Raimondo, A. & Valeri, D. Bethe Ansatz and the Spectral Theory of Affine Lie algebra–Valued Connections II: The Non Simply–Laced Case. Commun. Math. Phys. 349, 1063–1105 (2017). https://doi.org/10.1007/s00220-016-2744-2

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