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arXiv · 1512.07178

W-symmetry, topological vertex and affine Yangian

Tomáš Procházka
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Abstract

We discuss the representation theory of non-linear chiral algebra $\mathcal{W}_{1+\infty}$ of Gaberdiel and Gopakumar and its connection to Yangian of $\hat{\mathfrak{u}(1)}$ whose presentation was given by Tsymbaliuk. The characters of completely degenerate representations of $\mathcal{W}_{1+\infty}$ are for generic values of parameters 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 $\mathcal{W}_{1+\infty}$ picture turn out to have a simple combinatorial interpretation.

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Tomáš Procházka. 2019-07-17. W-symmetry, topological vertex and affine Yangian. https://doi.org/10.1007/jhep10(2016)077

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