Bernstein-Lunts等价性的一个简单证明

量子化包络代数的Beilinson-Bernstein对应

The Beilinson-Bernstein correspondence for quantized enveloping algebras

量子化旗流形的理论作为一个准方案（非交换方案）已经由伦茨-罗森伯格（Lunts-Rosenberg）发展。他们制定了一个类似的贝林森-伯恩斯坦对应使用$q$ -微分算子介绍了他们的早期文件。本文利用一类$q$ -微分算子建立了它的修正形式，它（可能）小于Lunts-Rosenberg所用的算子.

The characteristic variety of a generic foliation

We confirm a conjecture of Bernstein-Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.

Unitary equivalences for reductive p-adic groups

We establish a transfer of unitarity for a Bernstein component of the category of smooth representations of a reductive p-adic group to the associated Hecke algebra, in the framework of the theory of types, whenever the Hecke algebra is an affine Hecke algebra with geometric parameters, in the sense of Lusztig (possibly extended by a group of automorphisms of the root datum). It is known that there is a large class of such examples (detailed in the paper). As a consequence, we establish relations between the unitary duals of different groups, in the spirit of endoscopy.

Induction equivalence for equivariant D-modules on rigid analytic spaces

We prove an Induction Equivalence and a Kashiwara Equivalence for coadmissible equivariant D-modules on rigid analytic spaces. This allows us to completely classify such objects with support in a single orbit of a classical point with co-compact stabiliser. As an application, we use the locally analytic Beilinson-Bernstein equivalence to construct new examples of large families of topologically irreducible locally analytic representations of certain compact semisimple p-adic Lie groups.

关于 $p$-进域 $F$ 上 $\mathrm{GL}_n(F)$ ($n>2$) 的 Hecke 代数的一个问题

A problem on Hecke algebras for $\mathrm{GL}_n(F)$ for $n>2$ over $p$-adic field $F$

研究 $p$-进域上 $\mathrm{GL}_n$ ($n>2$) 的 Hecke 代数，通过 Bernstein 分解和交织代数证明不同域上的 Hecke 代数 Morita 等价。

有限W-代数的局部化定理

A Localization Theorem for Finite W-algebras

本文受Beilinson-Bernstein与Kashiwara-Rouquier启发，为有限W-代数上的模范畴提供几何解释，并借此重新证明Skryabin等价。