Elementary representations of the laguerre group

A class of representations of the Laguerre group in nuclear spaces is studied. The Laguerre group is the group of matrices of order two with determinant 1 over the ring of dual numbers. The question of irreducibility is considered, and a classification of bilinear invariant functionals, intertwining operators, and Hermitian invariant functionals is obtained.Translated from Matematicheskie Zametki, Vol. 23, No. 1, pp. 31–39, January, 1978.