Whittaker vectors for $\mathcal{W}$-algebras from topological recursion

Gaëtan Borot, Vincent Bouchard, Nitin Kumar Chidambaram +1

We identify Whittaker vectors for ${\mathcal{W}}_k(\mathfrak{g})$-modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundam…