Chekhov, Leonid and Mazzocco, Marta
(2011)
*Isomonodromic deformations and twisted Yangians
arising in TeichmÃ¼ller theory.*
Advances in Mathematics.
ISSN 0001-8708
(In Press)

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## Abstract

In this paper we build a link between the TeichmÃ¼ller theory of hyperbolic Riemann surfaces and isomonodromic deformations of linear systems whose monodromy group is the Fuchsian group associated to the given hyperbolic Riemann surface by the PoincarÃ© uniformization. In the case of a one-sheeted hyperboloid with n orbifold points we show that the Poisson algebra Dn of geodesic length functions is the semiclassical limit of the twisted q-Yangian Y q (on) for the orthogonal Lie algebra on defined by Molev, Ragoucy and Sorba. We give a representation of the braid-group action on Dn in terms of an adjoint matrix action. We characterize two types of finite-dimensional Poissonian reductions and give an explicit expression for the generating function of their central elements. Finally, we interpret the algebra Dn as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semi-simple point.

Item Type: | Article |
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Uncontrolled Keywords: | Braid group; Geodesic algebra; Fuchsian system; Frobenius manifold; Monodromy |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 14 Jan 2011 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/1562 |

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