Dual Baxter equations and quantization of Affine Jacobian

A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the eigen-functions of its Hamiltonians coincide with the eigen-functions of Hamiltonians of the original model. We explain that this duality can be considered as duality between homologies and cohomologies of quantized affine hyper-elliptic Jacobian.