Integrable systems on rectangular W-superalgebras via super Adler-type operators

2023/10/07 by Carpentier, Sylvain, Lee, Gahng Sahn, Suh, Uhi Rinn
#17B69 #17B80 #35Q53 (Primary) 37K10 #37K30 (Secondary) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2310.04661

Abstract

In this paper, we introduce a class of super Adler-type operators associated with the Lie superalgebra \mathfrakgl(m|n). We show that these operators generate Poisson vertex superalgebras which are isomorphic to the classical W-superalgebras associated with \mathfrakgl(m|n) and some rectangular nilpotent elements. We use this isomorphism to construct integrable hierarchies on these rectangular W-superalgebras.

Related

• Adler-Oevel-Ragnisco type operators and Poisson vertex algebras
• Structures of (supersymmetric) classical W-algebras
• Supersymmetric Bi-Hamiltonian Systems
• Gelfand-Dickey Realizations of the supersymmetric classical W-algebras for \mathfrakgl(n+1|n) and \mathfrakgl(n|n)
• Classcal affine W-algebras associated to Lie superalgebras