Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the discrete translation group we use the kernel of the Fourier transform. From the Dirac representation of the Lorentz group (including reflections) we derive in a natural way the wave equation on the lattice for spin 1/2 particles. Finally the induced representation of the discrete inhomogeneous Lorentz group is constructed by standard methods and its connection with the continuous case is discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission

An Aspect of Icosahedral Symmetry Dedicated to R.V. Moody on the occasion of his 60th birthday

Abstract. We embed the moduli space Q of 5 points on the projective line S5-equivariantly into P(V), where V is the 6-dimensional irreducible module of the symmetric group S5. This module splits with respect to the icosahedral group A5 into the two standard 3-dimensional representations. The resulting linear projections of Q relate the action of A5 on Q to those on the regular icosahedron