Yangians and $$\mathcal{W} $$ -Algebras

We present a connection between -algebras and Yangians in the case of gl(N) algebras, as well as for twisted Yangians and super-Yangians. We illustrate this connection, which allows constructing an R-matrix for the -algebras and classifying their finite-dimensional irreducible representations, in the framework of the nonlinear Schrödinger equation in 1+1 dimensions.