Stokes Multipliers, Spectral Determinants and T-Q relations

Recently, a remarkable correspondence has been unveiled between a certain class of ordinary linear differential equations (ODE) and integrable models. In the first part of the report, we survey the results concerning the 2nd order differential equations, the Schroedinger equation with a polynomial potential. We will observe that fundamental objects in the study of the solvable models, e.g., Baxter's Q- operator, fusion transfer matrices come into play in the analyses on ODE. The second part of the talk is devoted to the generalization to higher order linear differential equations. The correspondence found in the case of the 2nd order ODE is naturally lifted up. We also mention a connection to the discrete soliton theory.