2009/09/29 by Leonid Chekhov, Chekhov, Leonid, Marta Mazzocco +1 · 1 citation
Mathematics · Physics and Astronomy · #17B37 #17B63 #32G15 #32G34 #32G81 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.AG #math.DG #math.MP #msc:17B37 #msc:17B63 #msc:32G15 #msc:32G34 #msc:32G81
paper · pdf · doi:10.48550/arxiv.0909.5350
44 pages, 10 pictures
arxiv created 2009/09/29 · openalex publication_date 2009/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we build a link between the Teichmuller 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 Poincare' 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 for the orthogonal Lie algebra defined by Molev, Ragoucy and Sorba. We give a representation of the braid group action on this algebra 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-semisimple point.