An extension of the Borel-Weil construction to the quantum group \(U_ q(n)\)

DOI10.1007/BF02097014zbMath0757.17009OpenAlexW2025058578MaRDI QIDQ1198808

M. A. Lohe, L. C. Biedenharn

Publication date: 16 January 1993

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

Full work available at URL: https://doi.org/10.1007/bf02097014

zbMATH Keywords

quantum groupirreducible representationsBorel-Weil theorem

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)

Related Items

Coordinates of the quantum plane as \(q\)-tensor operators in \({\mathcal U}_q({\mathfrak su}(2) * {\mathfrak su}(2))\), Gauss decomposition for quantum groups and supergroups, Representation theory approach to the polynomial solutions of q-difference equations: Uq(sl(3)) and beyond, A Borel-Weil theorem for the quantum Grassmannians, Representations of 𝒰h (𝔰𝔲(N) ) derived from quantum flag manifolds, Yangian symmetric correlators, Polynomial realization of the Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis, Bott–Borel–Weil construction for quantum supergroup Uq(gl(m|n)), Factorization of the \(\mathcal R\)-matrix for the quantum algebra \({U_q(s\ell_3)}\), Factorization of the \(R\)-matrix for the quantum algebra \({U_q(s\ell_n)}\), Normalized Uq(sl(3)) Gel’fand–(Weyl)–Zetlin basis and new summation formulas for q-hypergeometric functions, Coherent states for quantum compact groups, SELF-SIMILARITY PROPERTIES OF NAFIONIZED AND FILTERED WATER AND DEFORMED COHERENT STATES, Iterative construction of \(U_q(\mathrm{sl}(n+1))\) representations and Lax matrix factorisation, A LERAY SPECTRAL SEQUENCE FOR NONCOMMUTATIVE DIFFERENTIAL FIBRATIONS, Vector coherent state realization of representations of the affine superalgebra A(1)(,1), A Borel-Weil-Bott approach to representations of \(\text{sl}_ q(2,\mathbb{C})\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homogeneous vector bundles
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• 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
• A q-analog of the Gauss summation theorem for hypergeometric series in U(n)
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• Implementation of the U(n) tensor operator calculus in a vector Bargmann Hilbert space
• The q-deformed boson realisation of the quantum group SU(n)_qand its representations
• The quantum group SU_q(2) and a q-analogue of the boson operators
• On the q oscillator and the quantum algebra su_q(1,1)
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Coherent states of the real symplectic group in a complex analytic parametrization. I. Unitary-operator coherent states
• Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34