2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/207897The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory. As a consequence, from purely group theoretical arguments we demonstrate that the eigenvalues must be right-eigenvalues and that the only consistent scalar products are the complex ones. We also define an explicit quaternion tensor product which leads to a set of additional group representations for integer ``spin''.28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di LecceHigh Energy Physics - Theorytext