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.
Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The Simply-Laced Case / Masoero, D.; Raimondo, A.; Valeri, D.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 344:3(2016), pp. 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
Valeri D.
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.| File | Dimensione | Formato | |
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