We assess the ODE/IM correspondence for the quantum g-KdV model, for a non-simply laced Lie algebra g. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra g(1), and constructing the relevant Ψ -system among subdominant solutions. We then use the Ψ -system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum 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
Masoero, D., Raimondo, A., Valeri, D. (2017). Bethe Ansatz and the Spectral Theory of Affine Lie algebra–Valued Connections II: The Non Simply–Laced Case. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 349(3), 1063-1105 [10.1007/s00220-016-2744-2].
Bethe Ansatz and the Spectral Theory of Affine Lie algebra–Valued Connections II: The Non Simply–Laced Case
Raimondo, A;
2017
Abstract
We assess the ODE/IM correspondence for the quantum g-KdV model, for a non-simply laced Lie algebra g. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra g(1), and constructing the relevant Ψ -system among subdominant solutions. We then use the Ψ -system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum 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 algebrasFile | Dimensione | Formato | |
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