On matrix elements of the -representation in a space of functions on -matrices

Abstract

ABSTRACTWe obtain matrix elements and kernel of representation operators for one realization of-representation in an appropriate space of functions defined on matrix cone. Indeed, we show that the matrix elements can be expressed in terms of product of two Gaussian hypergeometric functions and the kernel of integral operator corresponding to representation linear operator can be expressed in terms of Bessel functions of the first kind or modified Bessel functions of the second kind.