Representations of quantum matrix algebra M q(2) and its q-boson realization

DOI10.1063/1.529573zbMath0763.17013OpenAlexW1981590991MaRDI QIDQ4033963

Mo-Lin Ge, Chang-pu Sun, Xu-Feng Liu

Publication date: 16 May 1993

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

Full work available at URL: https://doi.org/10.1063/1.529573

zbMATH Keywords

quantum groupirreducible representationsindecomposable representationsquantum matrix algebra\(q\)-boson realization

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

Quantum matrices in \(N\) dimensions ⋮ Quantum chains with GLq(2) symmetry ⋮ 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 ⋮ On the Hochschild homology of smash biproducts ⋮ Colored solutions of the Yang–Baxter equation from representations of Uqgl(2) ⋮ The \(q\)-deformed vector and \(q\)-deformed outer product

Cites Work

• Irreducible representations of the quantum analogue of SU(2)
• An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Compact matrix pseudogroups
• Generalized chiral Potts models and minimal cyclic representations of \(U_ q (\widehat {\mathfrak gl}(n,C))\)
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• 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
• q-analogues of Verma representations of quantum algebras for q, a root of unity: the case of U_q(sl(3))