I will show that a discretization of Virasoro algebra naturally leads to an integrable system which is the Toda chain in the second Hamiltonian structure. After quantization we obtain a q-deformation of the Toda chain which is different from the standard q-Toda chain. I will present a modular invariant Baxter operator. I will sketch the solution of Baxter equation through the Non Linear Integral Equation technique, yielding modular invariant Bethe equations.

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