Unitary representations of the 2-dimensional Euclidean group in the   Heisenberg algebra
  E(2) is studied as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the unitary irreducible representations of the group are realized is explicitely constructed. The addition theorem for the Kummer functions is derived. 
H. Ahmedov and I. H. Duru