Geometry and Representations of the Quantum Supergroup OSPq(1|2n)

Details Geometry and Representations of the Quantum Supergroup OSPq(1|2n) Geometry and Representations of the Quantum Supergroup OSPq(1|2n)

1998-04-23

arxiv.org/abs/math/9804111v1

Mathematics

Quantum Algebra

Latex, 20 pages

Scientific paper

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.

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