Nearby cycles on Drinfeld-Gaitsgory-Vinberg Interpolation Grassmannian and long intertwining functor

Drinfeld-Gaitsgory-Vinberg 插值 Grassmannian 与几何 Satake 等价（附录由 Dennis Gaitsgory 撰写）

Drinfeld-Gaitsgory-Vinberg interpolation Grassmannian and geometric Satake equivalence (with appendix by Dennis Gaitsgory)

本文证明Schieder猜想，将仿射Grassmannian中相反半无限轨道交集的顶部紧支撑上同调形成的双代数等同于Langlands对偶正幂零子代数的泛包络代数，并构造其在几何Satake纤维函子上的作用，同时提出任意对称Kac-Moody情形的Coulomb分支构造。

Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg degeneration for SL_2

Let G be a reductive group and let Bun_G denote the moduli stack of G-bundles on a smooth projective curve. We begin the study of the singularities of a canonical compactification of Bun_G due to V. Drinfeld (unpublished), which we refer to as the Drinfeld-Lafforgue-Vinberg compactification. For G=GL_n certain smooth open substacks of this compactification have already appeared in the work of Drinfeld and of L. Lafforgue on the Langlands correspondence for function fields. The Drinfeld-Lafforgue-Vinberg compactification is however already singular for G=SL_2; questions about its singularities …

仿射李代数的修正正则表示所对应的顶点算子代数

Vertex operator algebras associated to modified regular representations of affine Lie algebras

设$G$是具有李代数$\mf g$的单复李群，$\af$是仿射李代数.利用交织算子和Knizhnik-Zamolodchikov方程构造了一族与$\mf g$相关的$\N$ -分次顶点算子代数.它们是$\af \oplus \af$ -在$k + \bar k = -2 h^\vee$的意义上的双级$k, \bar k \notin \Q$的模块，其中$h^\vee$是$\mf g$的双Coxeter数。它的共形权0分量是$G$上正则函数的代数。Arkhipov-Gaitsgory和Gorbounov-Malikov-Schechtman从不同的角度研究了这类顶点算子代数。我们证明了当$k$是无理数时，与$G$和水平$k$相关联的顶点代数体的顶点包络同构于我们上面构造的顶点算子代数。本文还讨论了积分中心电荷的情形。