Representations of the groups GL(n,R) and SU(n) in an SO(n) basis

Abstract
The explicit form for the infinitesimal operators and the (finite) matrix elements with respect to an SO(n) basis is obtained for the representations of the most degenerate series of the group SL(n,R), and for the irreducible unitary representations of the group SU(n) with highest weight (M,0,...,0).