Geometry and representations of the quantum supergroup OSPq(1|2n)
Abstract
The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter-Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of Connes' theory. Parabolic induction is developed by employing the quantum homogeneous supervector bundles. Quantum Frobenius reciprocity and a generalized Borel-Weil theorem are established for the induced representations.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- June 1999
- DOI:
- 10.1063/1.532882
- arXiv:
- arXiv:math/9804111
- Bibcode:
- 1999JMP....40.3175L
- Keywords:
-
- 11.30.Pb;
- 02.40.-k;
- 02.20.-a;
- Supersymmetry;
- Geometry differential geometry and topology;
- Group theory;
- Mathematics - Quantum Algebra;
- Mathematical Physics
- E-Print:
- Latex, 20 pages