Master analytic representations and unified representation theory of certain orthogonal and pseudo-orthogonal groups

Abstract

The representation theory of the groups SO(5),SO(4, 1),SO(6) and SO(5, 1) is studied using the method of Master Analytic Representations (MAR). It is shown that a single analytic expression for the matrix elements of the generators of SO(n+1) and SO(n, 1) in an SO(n) basis yields all the unitary representations (for n=4,5); and that the compact and non-compact groups have essentially the same analytic representation. Once the MAR of a group is worked out, the search for the unitary irreducible representations is reduced to a purely arithmetic operation. The utmost care has been exercised to conduct the discussions at an elementary level: knowledge of simple angular momentum theory is the only prerequisite.