• Corpus ID: 88516840

Higher Airy structures, W algebras and topological recursion

@article{Borot2018HigherAS,
  title={Higher Airy structures, W algebras and topological recursion},
  author={Gaetan Borot and Vincent Bouchard and Nitin Kumar Chidambaram and Thomas Creutzig and Dmitry Noshchenko},
  journal={arXiv: Mathematical Physics},
  year={2018}
}
We define higher quantum Airy structures as generalizations of the Kontsevich-Soibelman quantum Airy structures by allowing differential operators of arbitrary order (instead of only quadratic). We construct many classes of examples of higher quantum Airy structures as modules of $\mathcal{W}(\mathfrak{g})$ algebras at self-dual level, with $\mathfrak{g}= \mathfrak{gl}_{N+1}$, $\mathfrak{so}_{2 N }$ or $\mathfrak{e}_N$. We discuss their enumerative geometric meaning in the context of (open and… 
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