Geometry and representations of the quantum supergroup OSP (q)(1 vertical bar 2n)

The quantum supergroup OSPq(1\2n) is studied systematically. A Haar functio nal is constructed, and an algebraic version of the Peter-Weyl theory is ex tended to this quantum supergroup. Quantum homogeneous superspaces and quan tum homogeneous supervector bundles are defined following the strategy of C onnes' theory. Parabolic induction is developed by employing the quantum ho mogeneous supervector bundles. Quantum Frobenius reciprocity and a generali zed Borel-Weil theorem are established for the induced representations. (C) 1999 American Institute of Physics. [S0022-2488(99)00205-4].