Lattice integrals of motion of the Ising model on the cylinder

We consider the 2D critical Ising model with spatially periodic boundary conditions. It is shown that for a suitable reparameterization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable csc(4u)$csc\left(4u\right)$, u$u$ being the spectral parameter. The coefficients of this polynomial are decomposed on the periodic Temperley–Lieb algebra by introducing a lattice version of the local integrals of motion.