Interwinning operators for semisimple Lie groups

The unified expressions for interwining operators of the complex semisimple Lie groups and those of their real forms, whose rank equals real rank, has been obtained in the terms of invariant root technique, using universal parametrization and the method worked out earlier for construction of noncompact semisimple Lie operator-irreducible representations. The obtained expressions apparantly carry a mutual character which is confirmed by the considered example of U(p,q) group. The received expressions are products of operator-functions, that correspond to rank 1 subgroups, and contain complete information about analytic properties of interwinning operators in weight-space (in maximal compact subgroup generator basis) and, about all complete irreducible representation and their pseudo-unitary components