The quantum volterra model and the lattice sine-Gordon system. - Construction of the Baxter Q operator and the integrals of motion

We investigate the integrable structure of the quantum Volterra model, which is a discretization of the Korteweg-de Vries equation. Based on Sklyanin's method we derive the Baxter equation, and then clarify a role of the "fundamental transfer matrix". We show that the fundamental transfer matrix also generates the integrals of motion for a lattice analogue of the sine-Gordon system.