*Representations of a Quantum Heisenberg Group Algebra
Abstract
In our earlier work, we constructed a specific noncompact quantum group whose quantum group structures have been constructed on a certain twisted group C*algebra. In a sense, it may be considered as a ``quantum Heisenberg group C*algebra''. In this paper, we will find, up to equivalence, all of its irreducible *representations. We will point out the Kirillov type correspondence between the irreducible representations and the socalled ``dressing orbits''. By taking advantage of its comultiplication, we will then introduce and study the notion of ``inner tensor product representations''. We will show that the representation theory satisfies a ``quasitriangular'' type property, which does not appear in ordinary group representation theory.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.math/9812045
 arXiv:
 arXiv:math/9812045
 Bibcode:
 1998math.....12045K
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Quantum Algebra;
 46L87;
 81R50;
 22D25
 EPrint:
 AMS LaTeX, 24 pages. Revised from the previous version