Decomposition matrices for the square lattices of the Lie groups $$SU(2)\times SU(2)$$SU(2)×SU(2)
Mark Bodner, Zofia Grabowiecka, J. Patera, Marzena G Szajewska · Analysis and Mathematical Physics · 2019
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 \(SU(2)\times SU(2)\) or equivalently by the Lie algebra \(A_1\times A_1\) , or by the simple Lie group O (5) or its Lie algebra called \(C_2\) or equivalently \(B_2\) . 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.