Abstract
We discuss the representation theory of the non-linear chiral algebra \( {\mathcal{W}}_{1+\infty } \) of Gaberdiel and Gopakumar and its connection to the Yangian of \( \widehat{\mathfrak{u}(1)} \) whose presentation was given by Tsymbaliuk. The characters of completely degenerate representations of \( {\mathcal{W}}_{1+\infty } \) are given by the topological vertex. The Yangian picture provides an infinite number of commuting charges which can be explicitly diagonalized in \( {\mathcal{W}}_{1+\infty } \) highest weight representations. Many properties that are difficult to study in the \( {\mathcal{W}}_{1+\infty } \) picture turn out to have a simple combinatorial interpretation, once translated to the Yangian picture.
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Procházka, T. \( \mathcal{W} \) -symmetry, topological vertex and affine Yangian. J. High Energ. Phys. 2016, 77 (2016). https://doi.org/10.1007/JHEP10(2016)077
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DOI: https://doi.org/10.1007/JHEP10(2016)077