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

Summary
"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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More information & hyperlinks
Web resources: https://cordis.europa.eu/project/id/101002592
Start date: 01-09-2021
End date: 31-08-2026
Total budget - Public funding: 1 268 551,00 Euro - 1 268 551,00 Euro
Cordis data

Original description

"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)."

Status

SIGNED

Call topic

ERC-2020-COG

Update Date

27-04-2024
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Horizon 2020
H2020-EU.1. EXCELLENT SCIENCE
H2020-EU.1.1. EXCELLENT SCIENCE - European Research Council (ERC)
ERC-2020
ERC-2020-COG ERC CONSOLIDATOR GRANTS