We study the ODE/IM correspondence for ODE associated to g^ -valued connections, for a simply-laced Lie algebra 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.
Masoero, D., Raimondo, A., Valeri, D. (2016). Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The simply-laced Case. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 344(3), 719-750 [10.1007/s00220-016-2643-6].
Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The simply-laced Case
Raimondo A.;
2016
Abstract
We study the ODE/IM correspondence for ODE associated to g^ -valued connections, for a simply-laced Lie algebra 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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