Computing Green functions in small characteristics

Duration: 46 mins 55 secs

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Description:	Geck, M Monday 27th January 2020 - 10:10 to 11:00


Created:	2020-01-27 11:21
Collection:	Groups, representations and applications: new perspectives
Publisher:	Isaac Newton Institute
Copyright:	Geck, M
Language:	eng (English)


Abstract:	Green functions for finite groups of Lie type were introduced by Deligne and Lusztig in the 1970's, using cohomological methods. The computation of these functions is a crucial step in the more general programme of determining the whole character tables of those groups. Despite of a long tradition of work on Green functions, there are still open cases for groups in small characteristic. We report on some recent progress, which essentially relies on a combination of Lusztig's theory of character sheaves and computer algebra methods.

Abstract:

Green functions for finite groups of Lie type were introduced by Deligne and Lusztig in the 1970's, using cohomological methods. The computation of these functions is a crucial step in the more general programme of determining the whole character tables of those groups. Despite of a long tradition of work on Green functions, there are still open cases for groups in small characteristic. We report on some recent progress, which essentially relies on a combination of Lusztig's theory of character sheaves and computer algebra methods.

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