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On the representation theory of quantum Heisenberg group and algebra

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Czechoslovak Journal of Physics Aims and scope

Abstract

We show that the quantum Heisenberg groupH q (1) and its *-Hopf algebra structure can be obtained by means of contraction from quantumSU q (2) group. Its dual Hopf algebra is the quantum Heisenberg algebraU q (h(1)). We derive left and right regular representations forU q (h(1)) as acting on its dualH q (1). Imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. Realized in the Bargmann-Hilbert space of analytic functions the unitarity of regular representation is also shown. 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 group left representations leads to finite dimensional irreducible ones for which the intertwinning operator is also investigated.

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Authors and Affiliations

  1. Departamento de Fśica Teórica and IFIC, Centro Mixto Universidad de Valencia, CSIC, E-46100, Burjassot, Valencia, Spain

    Demosthenes Ellinas

  2. Institute of Theoretical Physics, Wroclaw University, Pl. Maxa Borna 9, 50-205, Wroclaw, Poland

    Jan Sobczy

Authors
  1. Demosthenes Ellinas
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  2. Jan Sobczy
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Supported by DGICYT of Spain.

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Ellinas, D., Sobczy, J. On the representation theory of quantum Heisenberg group and algebra. Czech J Phys 44, 1019–1027 (1994). https://doi.org/10.1007/BF01690454

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  • DOI: https://doi.org/10.1007/BF01690454

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