Solutions of the Kzb Equations in Genus Greater than One B. Enriquez and G. Felder
نویسندگان
چکیده
Introduction. The Knizhnik-Zamolodchikov-Bernard connection ([22, 5, 27]) can be viewed as a flat connection over the complement det∗g,ν of the zero-section in the total space of the determinant line bundle over the moduli space Mg,ν·12 of genus g curves with ν marked points and tangent vectors ([4]). Projectivization of this connection is the pull-back of a flat projective connection on Mg,ν·12. The aim of this paper is two-fold. We first construct a flat version of the KZB connection over the moduli space Mg,ν·12, when ν ≥ 1 (we will set ν = n+1). We then give integral formulas for flat sections of this connection, using the functional parametrization of conformal blocks and the KZB connection introduced in [9].
منابع مشابه
Hecke-tyurin Parametrization of the Hitchin and Kzb Systems
We study the parametrization of the moduli space Bun2(C)L of rank 2 bundles over a curve C with fixed determinant, provided by Hecke modifications at fixed points of the trivial bundle. This parametrization is closely related to the Tyurin parametrization of vector bundles over curves. We use it to parametrize the Hitchin and KZB systems, as well as lifts of the Beilinson-Drinfeld D-modules. We...
متن کاملCoinvariants for Yangian Doubles and Quantum Knizhnik-zamolodchikov Equations
We present a quantum version of the construction of the KZ system of equations as a flat connection on the spaces of coinvariants of representations of tensor products of Kac-Moody algebras. We consider here representations of a tensor product of Yangian doubles and compute the coinvariants of a deformation of the subalgebra generated by the regular functions of a rational curve with marked poi...
متن کاملExtremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations
In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.
متن کاملOne-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes
We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...
متن کامل