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 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 psi-system among subdominant solutions. We then use the psi-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.