Geometry of Quantum Homogeneous Supervector Bundles and Representation Theory of Quantum General Linear Supergroup

Details Geometry of Quantum Homogeneous Supervector Bundles and Representation Theory of Quantum General Linear Supergroup Geometry of Quantum Homogeneous Supervector Bundles and Representation Theory of Quantum General Linear Supergroup

1998-03-10

arxiv.org/abs/math/9803031v1

Mathematics

Quantum Algebra

To appear in the Proceedings of the Fifth International Wigner Symposium, 25-29 August 1997, Vienna

Scientific paper

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.

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