Summary
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).
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).
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More information & hyperlinks
| Web resources: | https://cordis.europa.eu/project/id/677147 |
| Start date: | 01-09-2016 |
| End date: | 31-08-2021 |
| Total budget - Public funding: | 882 843,75 Euro - 882 843,00 Euro |
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Original description
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).
Status
CLOSEDCall topic
ERC-StG-2015Update Date
27-04-2024
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