2020/01/16 by Valeri, Daniele
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2001.05751
W-algebras are certain algebraic structures associated to a finite dimensional Lie algebra \mathfrak g and a nilpotent element f via Hamiltonian reduction. In this note we give a review of a recent approach to the study of (classical affine and quantum finite) W-algebras based on the notion of Lax type operators. For a finite dimensional representation of \mathfrak g a Lax type operator for W-algebras is constructed using the theory of generalized quasideterminants. This operator carries several pieces of information about the structure and properties of the W-algebras and shows the deep connection of the theory of W-algebras with Yangians and integrable Hamiltonian hierarchies of Lax type equations.