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2011.6: Isomonodromic deformations and twisted Yangians arising in Teichmüller theory

2011.6: Leonid Chekhov and Marta Mazzocco (2011) Isomonodromic deformations and twisted Yangians arising in Teichmüller theory. Advances in Mathematics. ISSN 0001-8708

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DOI: 10.1016/j.aim.2010.12.017

Abstract

In this paper we build a link between the Teichmüller 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 Poincaré 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
Uncontrolled Keywords:Braid group; Geodesic algebra; Fuchsian system; Frobenius manifold; Monodromy
Subjects:MSC 2000 > 14 Algebraic geometry
MIMS number:2011.6
Deposited By:Ms Lucy van Russelt
Deposited On:14 January 2011

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