Commutant structuture of Ux...xUxU* transformations

In this paper we have found irreducible representations (irreps) of the algebra of partially transposed permutation operators on last subsystem. We give here direct method of irreps construction for an arbitrary number of subsystems n and local dimension d. Our method is inspired by representation theory of symmetric group S(n), theory of Brauer Algebras and Walled Brauer Algebras.