Geometry of Quantum Homogeneous Supervector Bundles and Representation Theory of Quantum General Linear Supergroup
نویسنده
چکیده
The quantum general linear supergroup GL q (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 GL q (m|n). Quantum Frobenius reciprocity is proven, and a Borel-Weil theorem is established for the covariant and contravariant tensor irreps.
منابع مشابه
Geometry and Representations of the Quantum Supergroup Osp
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 ...
متن کاملGeometry and representations of the quantum supergroup OSPq„1z2n..
The quantum supergroup OSPq(1u2n) 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 ...
متن کاملQuantum Superalgebra Representations on Cohomology Groups of Non-commutative Bundles
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic sub-supergroup to the category of locally finite modules of the quantum general linear supergroup. The right derived functors of this functor provides a form of D...
متن کاملStructure and Representations of the Quantum General Linear Supergroup
The structure and representations of the quantum general linear supergroup GLq(m|n) are studied systematically by investigating the Hopf superalgebra Gq of its representative functions. Gq is factorized into G π q G π̄ q , and a Peter Weyl basis is constructed for each factor. Parabolic induction for the quantum supergroup is developed. The underlying geometry of induced representations is discu...
متن کاملGEOMETRY Of QUANTUM HOMOGENEOUS VECTOR BUNDLES AND REPRESENTATION THEORY OF QUANTUM GROUPS I
Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections furnish projective modules over algebras of functions on quantum homogeneous spaces. Further properties of the quantum homogeneous vector bundles are invest...
متن کامل