Representations of SU(1,1) in Non-commutative Space Generated by the   Heisenberg Algebra
  SU(1,1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. The addition theorems are derived. 
H. Ahmedov and I. H. Duru