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Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The simply-laced Case

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We study the ODE/IM correspondence for ODE associated to \({\widehat{\mathfrak{g}}}\)-valued connections, for a simply-laced Lie algebra \({\mathfrak{g}}\). We prove that subdominant solutions to the ODE defined in different fundamental representations satisfy a set of quadratic equations called \({\Psi}\)-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.

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Correspondence to Davide Masoero.

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Communicated by N. Reshetikhin

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Masoero, D., Raimondo, A. & Valeri, D. Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The simply-laced Case. Commun. Math. Phys. 344, 719–750 (2016). https://doi.org/10.1007/s00220-016-2643-6

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  • DOI: https://doi.org/10.1007/s00220-016-2643-6

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