The Integrals of Motion for the Deformed W-Algebra $W_{qt}(s{l}_N^{)}$ II: Proof of the commutation relations

Abstract

We explicitly construct two classes of infinitly many commutative operators in terms of the deformed W-algebra $W_{qt}(s{l}_N^{)}$, and give proofs of the commutation relations of these operators. We call one of them local integrals of motion and the other nonlocal one, since they can be regarded as elliptic deformation of local and nonlocal integrals of motion for the $W_N$ algebra.

arXiv commentDedicated to Professor Tetsuji Miwa on the occasion on the 60th birthday

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Cited by in corpus (5)

• Integrals of motion from quantum toroidal algebras
• Quadratic relations of the deformed $W$-superalgebra ${\mathcal{W}}_{q,t}(A(M,N))$
• The $({\mathfrak{gl}}_m,{\mathfrak{gl}}_n$) duality in the quantum toroidal setting
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
• Wakimoto realization of the elliptic algebra $U_{q,p}(\widehat{s{l}_N})$