Representations of SU(1,1) in Non-commutative Space Generated by the Heisenberg Algebra

Abstract

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.

Latex, 8 pages

References in corpus (3)

• Unitary representations of the 2-dimensional Euclidean group in the Heisenberg algebra
• Green Function on the q-Symmetric Space SU_q(2)/U(1)
• Green function on the quantum plane

Cited by in corpus (1)

• Summation Formulas for the product of the q-Kummer Functions from $E_q(2)$