Bethe Ansatz and the Spectral Theory of Affine Lie algebra–Valued Connections II: The Non Simply–Laced Case

We assess the ODE/IM correspondence for the quantum $${\mathfrak{g}}$$g-KdV model, for a non-simply laced Lie algebra $${\mathfrak{g}}$$g. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra $${{\mathfrak{g}}^{(1)}}$$g(1), and constructing the relevant $${\Psi}$$Ψ-system among subdominant solutions. We then use the $${\Psi}$$Ψ-system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum $${\mathfrak{g}}$$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.