Tilting modules for reductive algebraic groups: characters and support varieties

TL;DR

This paper explores the representation theory of reductive algebraic groups over algebraically closed fields of positive characteristic, focusing on tilting modules, their characters, and support varieties, providing new insights into their structure.

Contribution

It presents new results on tilting modules for reductive algebraic groups, especially regarding their characters and support varieties, advancing understanding in positive characteristic settings.

Findings

New character formulas for tilting modules

Descriptions of support varieties for these modules

Enhanced understanding of their structural properties

Abstract

These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed fields of positive characteristic. These statements mainly concern tilting modules, in particular their characters and support varieties.