Quantum Heisenberg Group and Algebra: Contraction, Left and Right Regular Representations

Details Quantum Heisenberg Group and Algebra: Contraction, Left and Right Regular Representations Quantum Heisenberg Group and Algebra: Contraction, Left and Right Regular Representations

1994-06-17

arxiv.org/abs/hep-th/9406114v1

J.Math.Phys. 36 (1995) 1404-1412

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Written in Tex with Harvmac macro, FTUV/94-30

Scientific paper

10.1063/1.531129

We show that the quantum Heisenberg group $H_{q}(1)$ can be obtained by means of contraction from quantum $SU_q(2)$ group. Its dual Hopf algebra is the quantum Heisenberg algebra $U_{q}(h(1))$. We derive left and right regular representations for $U_{q}(h(1))$ as acting on its dual $H_{q}(1)$. 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.

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