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Modular representation theory of reductive algebraic groups and local Geometric Langlands duality

Project description

Study furthers understanding of the representation theory of reductive groups

Reductive groups, types of linear algebraic groups over a field, are central to the representation theory. The latter is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces and studies modules over these structures. Recent studies have revealed strong connections between the representation theory and local geometric Langlands duality. The EU-funded RedLang project aims to further understanding of the representation theory of reductive groups by leveraging recent advances in the field, especially those pertaining to the computation of character formulas for simple and indecomposable tilting modules.

Objective

"In the recent years the PI has been involved in several breakthrough results in the representation theory of reductive algebraic groups (in particular related to the computation of character formulas for simple and indecomposable tilting modules), obtained using various techniques (in particular geometry and categorification). The present proposal aims at:
1. exploring the new perspectives offered by these results, which go beyond the computation of characters, and by the techniques we have already developed;
2. developing new geometric tools to support these advances.

Our main geometric input will be the development of a modular Local Geometric Langlands duality, in the spirit of work of Bezrukavnikov for characteristic-0 coefficients, and of a modular ""ramified"" geometric Satake equivalence. We expect in particular applications in the study of tilting modules (e.g. their behaviour under restriction to reductive subgroups, and their multiplicative properties), and to the description of the center of the distribution algebra (with a view towards understanding the ""higher linkage"" phenomena)."

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Coordinator

UNIVERSITE CLERMONT AUVERGNE
Net EU contribution
€ 918 461,00
Address
49 bd francois mitterrand
63000 Clermont ferrand
France

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Region
Auvergne-Rhône-Alpes Auvergne Puy-de-Dôme
Activity type
Higher or Secondary Education Establishments
Links
Other funding
€ 0,00

Beneficiaries (2)