Models of Lie algebra sl(2,C) and special matrix functions by means of a matrix integral transformation

Abstract

In this paper, we present four models of irreducible representations of special complex Lie algebra s l ( 2 , C ) from the special matrix functions point of view. These models, which involve differential operators, are transformed into matrix difference–differential operators using an integral transformation motivated by the integral representation of beta matrix function. We also obtain the matrix identities involving one or two variable special matrix functions.