Quadratic relations of the deformed Wsuperalgebra {{W}}_{q,t}≤ft(A(M,N)\right)
Abstract
We find the free field construction of the basic Wcurrent and screening currents for the deformed Wsuperalgebra ${\mathcal{W}}_{q,t}\left(A(M,N)\right)$ associated with Lie superalgebra of type A(M, N). Using this free field construction, we introduce the higher Wcurrents and obtain a closed set of quadratic relations among them. These relations are independent of the choice of Dynkin diagrams for the Lie superalgebra A(M, N), though the screening currents are not. This allows us to define ${\mathcal{W}}_{q,t}\left(A(M,N)\right)$ by generators and relations.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 August 2021
 DOI:
 10.1088/17518121/ac129f
 arXiv:
 arXiv:2101.01110
 Bibcode:
 2021JPhA...54G5201K
 Keywords:

 deformed W algebra;
 Lie superalgebra A(M;
 N);
 quadratic relation;
 free field construction;
 vertex operator;
 exactly solvable model;
 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 81R12
 EPrint:
 28 pages, 35 figures. arXiv admin note: substantial text overlap with arXiv:1912.03096