Free Boson Realization of $U_q(\widehat{s{l}_N})$

Abstract

We construct a realization of the quantum affine algebra $U_q(\widehat{s{l}_N})$ of an arbitrary level $k$ in terms of free boson fields. In the $q\to 1$ limit this realization becomes the Wakimoto realization of $\widehat{s{l}_N}$. The screening currents and the vertex operators(primary fields) are also constructed; the former commutes with $U_q(\widehat{s{l}_N})$ modulo total difference, and the latter creates the $U_q(\widehat{s{l}_N})$ highest weight state from the vacuum state of the boson Fock space.

arXiv comment24 pages, LaTeX, RIMS-924, YITP/K-1018

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• Level-One Representations and Vertex Operators of Quantum Affine Superalgebra $U_q[\widehat{gl(N|N)}]$
• Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c)
• New ${\mathcal{W}}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\mathcal{A}}_{q,p}(\hat{s}l(2{)}_c)$
• Quantum Z-algebras and representations of quantum affine algebras
• Drinfeld Basis And a Nonclassical Free Boson Representation of Twisted Quantum Affine Superalgebra $U_q[osp(2|2{)}^{(2)}]$}
• hbar-(Yangian) Deformation of Miura Map and Virasoro Algebra
• Vertex Operators of $U_q[\widehat{gl(N|N)}]$ and Highest Weight Representations of $U_q[\widehat{gl(2|2)}]$
• Level-One Highest Weight Representations of $U_q[\widehat{gl(1|1)}]$ and Associated Vertex Operators
• Elliptic Deformed Superalgebra $u_{q,p}(\widehat{sl}(M|N))$
• On the Vertex Operators of the Elliptic Quantum Algebra $U_{q,p}(\widehat{s{l}_2}{)}_k$}
• Free Field Realization of Quantum Affine Superalgebra $U_q(\widehat{sl}(N|1))$
• The algebra A_{\hbar,η}(\hat{g}) and Infinite Hopf family of algebras
• $U_q[\widehat{sl(2|1)}]$ Vertex Operators, Screen Currents and Correlation Functions at Arbitrary Level
• Free Field Approach to Solutions of the Quantum Knizhnik-Zamolodchikov Equations
• A Bosonization of $U_q(\widehat{sl}(M|N))$
• Screenings and Vertex Operators of Quantum Superalgebra $U_q(\widehat{sl}(N|1))$
• Free boson representation of DY_{\hbar}(gl_N)_k
• On a Bosonic-Parafermionic Realization of $U_q(\widehat{sl(2)})$
• Hamiltonian Reduction and the Construction of q-Deformed Extensions of the Virasoro Algebra
• Wakimoto realization of the elliptic algebra $U_{q,p}(\widehat{s{l}_N})$
• From quantum to elliptic algebras
• Quantum Sugawara operators in type $A$
• The elliptic quantum algebra $U_{q,p}(\widehat{s{l}_N})$ and its vertex operators
• Bosonization and vertex operator of supersymmetry $u_q(\widehat{sl}(n|1))$ for level $k$