# Confluence on the Painlevé Monodromy Manifolds, their Poisson Structure and Quantisation

Abstract : In this paper we obtain a system of flat coordinates on the monodromy manifold of each of the Painlevé equations. This allows us to quantise such manifolds. We produce a quantum confluence procedure between cubics in such a way that quantisation and confluence commute. We also investigate the underlying cluster algebra structure and the relation to the versal deformations of singularities of type $D_4,A_3,A_2$, and $A_1$.
Mots-clés :
Type de document :
Pré-publication, Document de travail
Version 1, 16 pages, 3 figures. 2012
Domaine :

https://hal.archives-ouvertes.fr/hal-00776844
Soumis le : mercredi 16 janvier 2013 - 12:47:22
Dernière modification le : lundi 5 février 2018 - 15:00:03

### Identifiants

• HAL Id : hal-00776844, version 1
• ARXIV : 1212.6723

### Citation

Marta Mazzocco, Vladimir Rubtsov. Confluence on the Painlevé Monodromy Manifolds, their Poisson Structure and Quantisation. Version 1, 16 pages, 3 figures. 2012. 〈hal-00776844〉

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