  The quantum general linear supergroup GLq(m|n) is defined and its structure
is studied systematically. Quantum homogeneous supervector bundles are
introduced following Connes' theory, and applied to develop the representation
theory of GLq(m|n). Quantum Frobenius reciprocity is proven, and a Borel - Weil
theorem is established for the irreducible covariant and contravariant tensor
representations.
