W-symmetry, topological vertex and afline Yangian

We discuss the representation theory of the non-linear chiral algebra W1+infinity, of Gaberdiel and Gopakumar and its connection to the Yangian of <(u(1))over cap> whose presentation was given by Tsymbaliuk. The characters of completely degenerate representations of W1+infinity are given by the topological vertex. The Yangian picture provides an infinite number of commuting charges which can be explicitly diagonalized in W1+infinity highest weight representations. Many properties that are difficult to study in the W1+infinity picture turn out to have a simple combinatorial interpretation, once translated to the Yangian picture.