Determinant bundle in a family of curves, after A. Beilinson and V. Schechtman

Beilinson–Schechtman 定理的一个抛物类比

A parabolic analog of a theorem of Beilinson and Schechtman

本文针对单连通单复群 G，建立抛物 G-丛模空间上抛物上同调行列式线丛 Atiyah 类的显式计算公式，从而推广 Beilinson–Schechtman 的既有定理。

Relative Algebraic Differential Characters

Let $f: X \to S$ be a smooth morphism in characteristic 0, and let $(E, \nabla_{X/S})$ be a relative regular connection. We define a cohomology of relative differential characters on $X$ which receives classes of $(E, \nabla_{X/S})$. It says in particular that the partial vanishing of the trace of the iterated Atiyah classs can be made canonical. While applied to a family of curves and $c_2$, the construction yields a connection of $f_*c_2(E)$. This one has been constructed analytically by A. Beilinson. We also relate our construction to the trace complex of Beilinson of Schechtman.

Beilinson-Drinfeld Schubert varieties and global Demazure modules

We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson- Drinfeld affine Grassmannians. The answer is given in terms of global Demazure modules over the current Lie algebra.

Hecke-Tyurin parametrization of the Hitchin and KZB systems

We study the parametrization of the moduli space Bun_2(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 express a generating series for the lifts of the Beilinson-Drinfeld operators in terms of a "quantum L-operator" \ell(z). We explain the relation to earlier joint work with G. Felder, based on paramet…