Abelian representation for the non-Abelian Wilson loop and the non-Abelian Stokes theorem on the lattice

We derive the Abelian-like expression for the lattice SU(N) Wilson loop in an arbitrary irreducible representation. The continuum Abelian representation of the SU(N) Wilson loop (for the loop without selfintersections) that has been obtained by Diakonov and Petrov appears to be a continuum limit of this expression. We also obtain the lattice variant of a non-Abelian Stokes theorem and present the explicit expression for the matrix H used in the Diakonov-Petrov approach.