Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (892 kB)
References:
PDF
HTML
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}
Linking options:
  • https://www.mathnet.ru/eng/sigma1868
  • https://www.mathnet.ru/eng/sigma/v18/p72
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:35
    Full-text PDF :51
    References:10
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024