Quasi-derivations on 𝑈𝔤𝔩_{𝔫} and the argument shift method

Abstract

This paper surveys various properties of the quasi-derivations of the universal enveloping algebra U g l n U\mathfrak {gl}_n (over real or complex field) introduced by Gurevich, Pyatov and Saponov. We reinterprete these maps in terms of the algebraic operations on U g l n U\mathfrak {gl}_n and differential operators on G L n GL_n . We also describe the role of these operators in the attempts to implement the argument shifting procedure on U g l n U\mathfrak {gl}_n .