We will be looking at computing the correlation functions for the two-dimensional Ising model on a lattice with periodic boundary conditions. We will show how this problem can be reduced to a representation-theoretic problem associated with the orthogonal group. We determine formulas for the spin correlation function that depend on the matrix elements of the induced rotation associated with the spin operator. The representation of the spin-matrix elements is obtained by considering the spin operator as an intertwining map. Finally, we discuss how we can control the scaling limit of the multispin Ising correlations on the cylinder as the temperature approaches the critical temperature from below in terms of a Bugrij-Lisovyy conjecture for the spin matrix elements on the finite periodic lattice.