Irreducible representations of Hilbert C*-modules

The subject of the paper is representations of Hilbert C*-modules. We introduce the concept of a nondegenerate, irreducible and cyclic representation and the cornmutant of a Hilbert C*-module. Relations between representations of a Hilbert C*-module, its linking algebra and underlying C*-algebras are discussed. We also study Hilbert CCR-and GCR-modules and extend some results from CCR-and GCR algebras. The results we obtain are similar to the results known for C*-algebras.