Hecke-tyurin Parametrization of the Hitchin and Kzb Systems

Hitchin systems on ll-curves

R-Matrix Structure of Hitchin System in Tyurin Parameterization

We present a classical r-matrix for the Hitchin system without marked points on an arbitrary non-degenerate algebraic curve of genus g ≥ 2 using Tyurin parameterization of holomorphic vector bundles.

m at h . A G ] 1 8 A ug 2 00 8 PRYM - TYURIN VARIETIES VIA HECKE ALGEBRAS

Let G denote a finite group and π : Z → Y a Galois covering of smooth projective curves with Galois group G. For every subgroup H of G there is a canonical action of the corresponding Hecke algebra Q[H\G/H ] on the Jacobian of the curve X = Z/H . To each rational irreducible representation W of G we associate an idempotent in the Hecke algebra, which induces a correspondence of the curve X and ...

Solutions of the Kzb Equations in Genus Greater than One B. Enriquez and G. Felder

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·1...

On the link between the structure of A-branes observed in the homological mirror symmetry . . .

This paper is a review of some interesting results that has been obtained in the study of the categories of A-branes on the dual Hitchin fibers and some interesting phenomena associated with the endoscopy in the geometric Langlands correspondence of various authoritative theoretical physicists and mathematicians. The geometric Langlands correspondence has been interpreted as the mirror symmetry...