QUANTUM HEISENBERG-GROUP AND ALGEBRA - CONTRACTION, LEFT AND RIGHT REGULAR REPRESENTATIONS

It is shown that the quantum Heisenberg group Hq(1) can be obtained by means of contraction from the quantum SUq(2) group. Its dual Hopf algebra is the quantum Heisenberg algebra Uq(h(1)). Left and right regular representations for Uq(H(1)) as acting on its dual Hq(1) are derived. By imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. By duality, left and right regular representations for quantum Heisenberg group, with the quantum Heisenberg algebra as a representation module are also constructed. As before, the reduction of left representations leads to finite-dimensional irreducible ones for which the intertwining operator is also investigated. © 1995 American Institute of Physics.