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We discuss the representation theory of the non-linear chiral algebraW1+1of Gaberdiel and Gopakumar and its connection to the Yangian ofdu(1) whose presenta-tion was given by Tsymbaliuk. The characters of completely degenerate representations ofW1+1are given by the topological vertex. The Yangian picture provides an in nite num-ber of commuting charges which can be explicitly diagonalized inW1+1highest weightrepresentations. Many properties that are dicult to study in theW1+1picture turn outto have a simple combinatorial interpretation, once translated to the Yangian picture.
Description
An example of a rhombic tiling of plane which corresponds to a plane partition withthree boxes. Apart from 4-valent vertices, there are six trivalent vertices and ve 5-valent vertices.