Irreducible highest weight representations of quantum groups \(U_ q(gl(n,\mathbb{C}{}))\)
type: Item
instance of: scholarly article
title: Irreducible highest weight representations of quantum groups \(U_ q(gl(n,\mathbb{C}{}))\)
zbMATH Open document ID: 0764.17008
DOI: 10.1007/BF02100869
author: A. Vančura
author: Č. Burdík
author: M. Havlíček
published in: Communications in Mathematical Physics
publication date: 1993-01-16T00:00:00Z
review text: Let \(V\) be a module for the quantum algebra \(U_ q(gl(n,\mathbb{C}))\), and \({\mathcal F}_ n\) the \(n\)-fold tensor product of the Fock space. Then the authors give a representation of \(U_ q(gl(n+1,\mathbb{C}))\) on the space \({\mathcal F}_ n\otimes V\). Using this recurrence, irreducible highest weight representations of \(U_ q(gl(n,\mathbb{C}))\) are obtained.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 95438
zbMATH Keywords: quantum group
zbMATH Keywords: Fock space representation
zbMATH Keywords: irreducible highest weight representations
MaRDI profile type: Publication
cites work: The quantum group SUq(2) and a q-analogue of the boson operators
cites work: On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q
cites work: A new method of determining an irreducible representation of quantum Slq(3) algebra (I)
cites work: The q-analog of the boson algebra, its representation on the Fock space, and applications to the quantum group
cites work: Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
cites work: Quantum deformations of certain simple modules over enveloping algebras
cites work: A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
cites work: Realisations of the real semisimple Lie algebras: a method of construction
cites work: Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
cites work: The q-deformed boson realisation of the quantum group SU(n)qand its representations
cites work: Q4141356
cites work: Matrix canonical realizations of the Lie algebra u(p,q)
cites work: Periodic and partially periodic representations of \(\text{SU}(N)_ q\)
full work available at URL: https://doi.org/10.1007/bf02100869
OpenAlex ID: W2007972104
description: scientific article; zbMATH DE number 95438