Unitary representations of the 2-dimensional Euclidean group in the Heisenberg algebra

Abstract

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.

Latex, 6 pp

References in corpus (2)

• Green Function on the q-Symmetric Space SU_q(2)/U(1)
• Green function on the quantum plane

Cited by in corpus (2)

• Representations of SU(1,1) in Non-commutative Space Generated by the Heisenberg Algebra
• Summation Formulas for the product of the q-Kummer Functions from $E_q(2)$