Lattice Integrals of Motion of the Ising Model on the Strip

We consider the 2D critical Ising model on a strip with fixed boundary conditions. It is shown that for a suitable reparametrization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable $\csc(4u)$, being $u$ the spectral parameter. The coefficients of this polynomial are decomposed on the fixed boundaries Temperley-Lieb Algebra by introducing a lattice version of the Local Integrals of Motion.