# Higher Airy structures and topological recursion for singular spectral curves

@article{Borot2020HigherAS, title={Higher Airy structures and topological recursion for singular spectral curves}, author={Gaetan Borot and Reinier Kramer and Yannik Schuler}, journal={arXiv: Mathematical Physics}, year={2020} }

We give elements towards the classification of quantum Airy structures based on the $W(\mathfrak{gl}_r)$-algebras at self-dual level based on twisted modules of the Heisenberg VOA of $\mathfrak{gl}_r$ for twists by arbitrary elements of the Weyl group $\mathfrak{S}_{r}$. In particular, we construct a large class of such quantum Airy structures. We show that the system of linear ODEs forming the quantum Airy structure and determining uniquely its partition function is equivalent to a topological…

## 6 Citations

### Airy ideals, transvections and $\mathcal{W}(\mathfrak{sp}_{2N})$-algebras

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. In the ﬁrst part of the paper we propose a diﬀerent viewpoint on the theory of higher Airy structures (or Airy ideals) which may shed light on its origin. We deﬁne Airy ideals in the ~ -adic…

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Ordinary maps satisfy topological recursion for a certain spectral curve (x,y). We solve a conjecture from [5] that claims that fully simple maps, which are maps with non selfintersecting disjoint…

### Topological recursion for fully simple maps from ciliated maps

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Ordinary maps satisfy topological recursion for a certain spectral curve (x,y). We solve a conjecture from [5] that claims that fully simple maps, which are maps with non selfintersecting disjoint…

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