Kronecker product decomposition for Poincaré-like groups I. A general constructive method

For Poincaré-like groupsW=T×G, i.e. such Type I-groups which are semidirect products of a regularity embedded abelian normal subgroupT with a locally compact groupG, the problem of the Kronecker product decomposition has been solved, in the framework of induced representations theory, up to a reduction of little group representations. For practical applications some computational hints are given.The autors would like to thank Prof. H.Boseck, Dr. J.Niederle and Dr. J.Tolar for helpful and interesting discussions. One of us (Th. G.) would also like to thank Dr. J.Tolar for his kind hospitality during a stay at the Czech Technical University, Prague.