Misra, GadadharGadadharMisraNarayanan, E. K.E. K.NarayananVarughese, CherianCherianVarughese2025-08-312025-08-312024-09-0110.1007/s13226-024-00644-x2-s2.0-85197683242http://repository.iitgn.ac.in/handle/IITG2025/28768In this semi-expository article, we investigate the relationship between the imprimitivity introduced by Mackey several decades ago and commuting d- tuples of homogeneous normal operators. The Hahn–Hellinger theorem gives a canonical decomposition of a ∗- algebra representation ρ of C<inf>0</inf>(S) (where S is a locally compact Hausdorff space) into a direct sum. If there is a group G acting transitively on S and is adapted to the ∗- representation ρ via a unitary representation U of the group G, in other words, if there is an imprimitivity, then the Hahn–Hellinger decomposition reduces to just one component, and the group representation U becomes an induced representation, which is Mackey’s imprimitivity theorem. We consider the case where a compact topological space S⊂C^d decomposes into finitely many G- orbits. In such cases, the imprimitivity based on S admits a decomposition as a direct sum of imprimitivities based on these orbits. This decomposition leads to a correspondence with homogeneous normal tuples whose joint spectrum is precisely the closure of G- orbits.false22D45 | 47B15 | homogeneous operator | imprimitivity | induced representation | Primary 22D30Article097574651010-1025September 20240arJournal0WOS:001263682600001