Orthogonal polynomial expansions for finite group transformations

Yorck Leschber, Louisiana State University
J. P. Draayer, Louisiana State University
G. Rosensteel, Louisiana State University


A simple tractable method for calculating finite group transformations is given. This is achieved by introducing orthogonal polynomial functions of the generating element of the transformation. The polynomials, which are finite in number because the Cayley- Hamilton theorem applies, depend only on the conjugacy class of the transformation. Orthogonality is defined with respect to the trace operation. Results for SU(2) and the defining representation of SU(3) are examined in some detail. © 1986 IOP Publishing Ltd.