Decomposition matrices for the square lattices of the Lie groups $$SU(2)\\times SU(2)$$SU(2)×SU(2)

Abstract

A method for the decomposition of data functions sampled on a finite fragment of rectangular lattice is described. The symmetry of a square lattice in a 2-dimensional real Euclidean space is either given by the semisimple Lie group $$SU(2)\\times SU(2)$$SU(2)×SU(2) or equivalently by the Lie algebra $$A_1\\times A_1$$A1×A1, or by the simple Lie group O(5) or its Lie algebra called $$C_2$$C2 or equivalently $$B_2$$B2. In this paper we consider the first of these possibilities which is applied to data which is given in 2 orthogonal directions—hence the method is a concatenation of two 1-dimensional cases. The asymmetry we underline here is a different density of discrete data points in the two orthogonal directions which cannot be studied with the simple Lie group symmetry.