GEOMETRY OF QUANTUM HOMOGENEOUS VECTOR BUNDLES AND REPRESENTATION THEORY OF QUANTUM GROUPS I

DOI10.1142/S0129055X99000209zbMath0990.17013arXivq-alg/9705016MaRDI QIDQ4519807

A. Rod Gover, Ruibin Zhang

Publication date: 4 December 2000

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9705016

zbMATH Keywords

projective modulesquantum homogeneous spacesalgebras of functionsinduced representations of quantum groupsWoronowicz type compact quantum groups

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Geometry of quantum groups (58B32)

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The Dirac operator on \(\text{SU}_{q}(2)\) ⋮ Quantum superalgebra representations on cohomology groups of non-commutative bundles ⋮ A quantum analogue of the first fundamental theorem of classical invariant theory ⋮ A Borel-Weil theorem for the quantum Grassmannians ⋮ Dual canonical bases for the quantum special linear group and invariant subalgebras ⋮ Spherical functions on homogeneous superspaces ⋮ Noncommutative Riemannian and spin geometry of the standard \(q\)-sphere ⋮ Noncommutative fields and actions of twisted Poincaré algebra

Cites Work

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• Coherent states for quantum compact groups
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Compact matrix pseudogroups
• Representation theory of Hopf Galois extensions
• Structure and representations of the quantum general linear supergroup
• On the quantum flag manifold
• Quantum homogeneous spaces, duality and quantum 2-spheres
• CQG algebras: A direct algebraic approach to compact quantum groups
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Representations of quantum algebras

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