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arXiv · 1501.07421

Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case

Davide Masoero·Andrea Raimondo·Daniele Valeri
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Abstract

We study the ODE/IM correspondence for ODE associated to $\hat{\mathfrak g}$-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 $Ψ$-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.

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Davide Masoero, Andrea Raimondo, Daniele Valeri. 2016-06-16. Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case. https://doi.org/10.1007/s00220-016-2643-6

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