A quantum analog of the 𝒵 algebra

DOI10.1063/1.531581zbMath0871.17008arXivq-alg/9504009OpenAlexW2049517605MaRDI QIDQ5284805

Luc Vinet, A. Hamid Bougourzi

Publication date: 18 September 1997

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

Full work available at URL: https://arxiv.org/abs/q-alg/9504009

zbMATH Keywords

representationquantum affine algebraDrinfeld realization\({\mathcal Z}_ q\) algebraexplicit bases for \({\mathcal Z}_ q\) generalized Verma modulesquantum analog of Heisenberg algebra

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) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (2)

Quantum z-algebras and representations of quantum affine algebras ⋮ Elliptic algebra \(U_{q,p}(\hat{\mathfrak {g}})\) and quantum \(Z\)-algebras

Cites Work

• Vertex operator representations of the quantum affine algebra \(U_ q(B_ r^{(1)})\)
• The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum deformations of certain simple modules over enveloping algebras
• Diagonalization of the \(XXZ\) Hamiltonian by vertex operators
• On a bosonic-parafermionic realization of \(\text{U}_q(\widehat{\text{sl}(2)})\)
• \(N\)-point correlation functions of the spin-\(1\) \(XXZ\) model
• Vertex representations of quantum affine algebras

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