Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case (Q2630721)

In physics, the ODE/IM correspondence concerns the relations between the generalized spectral problems of linear ordinary differential equations (ODEs) and the two-dimensional integrable quantum field theory (QFT). In the present paper, the authors derive the ODE/IM correspondence for a simply laced Lie algebra in which case the affine Lie algebra is exactly its Langlands dual. They recall some prerequisites on finite-dimensional Lie algebras, prove the main results, derive the Bethe ansatz equation, and then some mathematical complements follow.