Representations of 𝒰h (𝔰𝔲(N) ) derived from quantum flag manifolds

DOI10.1063/1.531808zbMath0883.17019arXivq-alg/9610027OpenAlexW3106820491MaRDI QIDQ4338366

Pavel Šťovíček, Reidun Twarock

Publication date: 8 March 1998

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

Full work available at URL: https://arxiv.org/abs/q-alg/9610027

zbMATH Keywords

generatorsirreducible representationsdiagonalizationquantum Grassmanniansquantum flag manifold

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) Noncommutative topology (46L85) Noncommutative differential geometry (46L87)

Related Items (1)

``Classical flag varieties for quantum groups: the standard quantum \(\text{SL}(n,{\mathbb C})\).

Cites Work

• Coherent states for quantum compact groups
• q-Weyl group and a multiplicative formula for universal R-matrices
• Some applications of the quantum Weyl groups
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum R matrix for the generalized Toda system
• Quantum spheres
• Quantum deformations of certain simple modules over enveloping algebras
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Quantum deformation of flag schemes and Grassmann schemes. I: A \(q\)- deformation of the shape-algebra for \(GL(n)\)
• Universal \(R\)-matrix for quantized (super)algebras
• Differential calculus on quantized simple Lie groups
• An extension of the Borel-Weil construction to the quantum group \(U_ q(n)\)
• Quantum group gauge theory on quantum spaces
• Quantum Grassmann manifolds
• On the quantum flag manifold
• Quantum dressing orbits on compact groups
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Realization of \(U_ q(so(N))\) within the differential algebra on \(\mathbb{R}_ q^ N\)
• Antiholomorphic representations for orthogonal and symplectic quantum groups
• Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere
• Quantum line bundles on S2 and method of orbits for SUq(2)
• SU3 coherent state operators and invariant correlation functions and their quantum group counterparts
• On Fock-space representations of quantized enveloping algebras related to noncommutative differential geometry

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