Speaker: Roman Bezrukavnikov (MIT)

In person or on Zoom: https://mit.zoom.us/j/92441268505

Title: Classical limit of category O via positive characteristic

Abstract: Localization theorem identifies the category of modules over a semi-simple Lie algebra with D-modules, which can be thought of as a quantization of the cotangent bundle. A surprising observation is that in some cases of interest such category O and the category of (g,K) modules for quasi-split groups (conjecturally in general) the de-quantization contains the original category as a full subcategory. I will describe a strategy for proof via positive characteristic by a version of Deligne-Illusie method, lifting the D-modules to what one can call a Fontaine-Laffaille module. Based on a joint work in progress with A. Ionov and D. Davis.