The Drinfeld realization of the elliptic quantum group Bq,λ(A2(2))

DOI10.1063/1.1767296zbMath1071.17014arXivmath/0401055OpenAlexW1667972923MaRDI QIDQ4833474

Hitoshi Konno, Takeo Kojima

Publication date: 15 December 2004

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

Full work available at URL: https://arxiv.org/abs/math/0401055

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 (5)

Commutation relations of vertex operators for Uq(sl^(M|N)) ⋮ Elliptic quantum toroidal algebra \(U_{q,t,p}(\mathfrak{gl}_{1,tor})\) and affine quiver gauge theories ⋮ Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(A2(2)) ⋮ Elliptic quantum group \(U_{q,p}(\widehat{\mathfrak{sl}}_2)\), Hopf algebroid structure and elliptic hypergeometric series ⋮ The q-Wakimoto Realization of the Superalgebras $$U_{q}(\widehat{sl}(N|1))$$ and $$U_{q,p}(\widehat{sl}(N|1))$$

Cites Work

• Central extensions of quantum current groups
• Quantum affine algebras and holonomic difference equations
• Elliptic algebra \({\mathcal A}_{q,p}(\widehat{\mathfrak sl}_2)\) in the scaling limit
• Elliptic algebra \(U_{q,p} (\widehat {\mathfrak {sl}}_2)\): Drinfeld currents and vertex operators
• An elliptic algebra \(U_{q,p}(\widehat{\text{sl}_2})\) and the fusion RSOS model
• Elliptic quantum groups \(E_{\tau,\eta}({\mathfrak sl}_2)\) and quasi-Hopf algebras
• An elliptic quantum algebra for \(\widehat{\text{sl}}_ 2\)
• Quasi-Hopf deformations of quantum groups
• A coset-type construction for the deformed Virasoro algebra
• The elliptic algebra \(U_{q,p}(\widehat{\mathfrak{sl}}_N)\) and the Drinfeld realization of the elliptic quantum group \(\mathcal B_{q,\lambda}(\widehat{\mathfrak{sl}}_N)\).
• The twisted quantum affine algebra \(U_ q(A^{(2)}_ 2)\) and correlation functions of the Izergin-Korepin model.
• Order parameters of the dilute A models
• Quasi-Hopf twistors for elliptic quantum groups
• Creation/annihilation operators and form factors of the \(XXZ\) model
• Vertex operators for twisted quantum affine algebras
• Free field approach to the dilute AL models
• The elliptic algebra and the deformation ofW_Nalgebra
• THE QUANTUM KNIZHNIK–ZAMOLODCHIKOV EQUATION ASSOCIATED WITH $U_q(A_2^{(2)})$ FOR |q| = 1
• New construction of solvable lattice models including an Ising model in a field

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