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Quadratic Relations of the Deformed $W$-Algebra for the Twisted Affine Lie Algebra of Type $A_{2N}^{(2)}$
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We revisit the free field construction of the deformed $W$-algebra by Frenkel and Reshetikhin [Comm. Math. Phys. 197 (1998), 1–32], where the basic $W$-current has been identified. Herein, we establish a free field construction of higher $W$-currents of the deformed $W$-algebra associated with the twisted affine Lie algebra $A_{2N}^{(2)}$. We obtain a closed set of quadratic relations and duality, which allows us to define deformed $W$-algebra ${\mathcal W}_{x,r}\big(A_{2N}^{(2)}\big)$ using generators and relations.
Keywords: deformed $W$-algebra, twisted affine algebra, quadratic relation, free field construction, exactly solvable model. 
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     author = {Takeo Kojima},
     title = {Quadratic {Relations} of the {Deformed} $W${-Algebra} for the {Twisted} {Affine} {Lie} {Algebra} of {Type} $A_{2N}^{(2)}$},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a71/}
}
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Takeo Kojima. Quadratic Relations of the Deformed $W$-Algebra for the Twisted Affine Lie Algebra of Type $A_{2N}^{(2)}$. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a71/

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