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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 072, 36 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.072 (Mi sigma1868) 		 
Quadratic Relations of the Deformed $W$-Algebra for the Twisted Affine Lie Algebra of Type $A_{2N}^{(2)}$

Takeo Kojima

Department of Mathematics and Physics, Faculty of Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan
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DOI: https://doi.org/10.3842/SIGMA.2022.072
Abstract: 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.
Funding agency Grant number
Japan Society for the Promotion of Science JP19K03509
This work was supported by JSPS KAKENHI (Grant Number JP19K03509).
Received: December 15, 2021; in final form September 9, 2022; Published online October 4, 2022
Bibliographic databases:
Document Type: Article
MSC: 81R10, 81R12, 81R50, 81T40, 81U15
Language: English
Citation: Takeo Kojima, “Quadratic Relations of the Deformed $W$-Algebra for the Twisted Affine Lie Algebra of Type $A_{2N}^{(2)}$”, SIGMA, 18 (2022), 072, 36 pp.
Citation in format AMSBIB
\Bibitem{Koj22}
\by Takeo~Kojima
\paper Quadratic Relations of the Deformed $W$-Algebra for the Twisted Affine Lie Algebra of Type $A_{2N}^{(2)}$
\jour SIGMA
\yr 2022
\vol 18
\papernumber 072
\totalpages 36
\mathnet{http://mi.mathnet.ru/sigma1868}
\crossref{https://doi.org/10.3842/SIGMA.2022.072}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4491638}
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