Quantum Heisenberg Group and Algebra : Contraction , Left and Right Regular Representations
نویسنده
چکیده
We show that the quantum Heisenberg group Hq(1) can be obtained by means of contraction from quantum SUq(2) group. Its dual Hopf algebra is the quantum Heisenberg algebra Uq(h(1)). We derive left and right regular representations for Uq(h(1)) as acting on its dual Hq(1). 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 representation module are also constructed. As before reduction of left representations leads to finite dimensional irreducible ones for which the intertwinning operator is also investigated. 1 e-mail: [email protected] ; supported by DGICYT Spain 2 permanent address: Institute of Theoretical Physics, Wroc law University, Pl. Maxa Borna 9, 50-205, Wroc law, Poland; e-mail: [email protected] ; supported by EEC grant ERBCIPACT920488
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