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ModRed

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The geometry of modular representations of reductive algebraic groups
The main theme of this proposal is the Geometric Representation Theory of reductive algebraic groups over algebraically closed fields of positive characteristic. Our primary goal is to obtain character formulas for simple and for... The main theme of this proposal is the Geometric Representation Theory of reductive algebraic groups over algebraically closed fields of positive characteristic. Our primary goal is to obtain character formulas for simple and for indecomposable tilting representations of such groups, by developing a geometric framework for their categories of representations. Obtaining such formulas has been one of the main problems in this area since the 1980's. A program outlined by G. Lusztig in the 1990's has lead to a formula for the characters of simple representations in the case the characteristic of the base field is bigger than an explicit but huge bound. A recent breakthrough due to G. Williamson has shown that this formula cannot hold for smaller characteristics, however. Nothing is known about characters of tilting modules in general (except for a conjectural formula for some characters, due to Andersen). Our main tools include a new perspective on Soergel bimodules offered by the study of parity sheaves (introduced by Juteau-Mautner-Williamson) and a diagrammatic presentation of their category (due to Elias-Williamson). ver más
31/08/2021
UCA
883K€
Duración del proyecto: 68 meses Fecha Inicio: 2015-12-18
Fecha Fin: 2021-08-31

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2021-08-31
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-StG-2015: ERC Starting Grant
Cerrada hace 9 años
Presupuesto El presupuesto total del proyecto asciende a 883K€
Líder del proyecto
UNIVERSITE CLERMONT AUVERGNE No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5