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SUMMARY:Characters and character sheaves of finite groups of Lie type - Jo
 nas Hetz (Universität Stuttgart)
DTSTART:20220519T150000Z
DTEND:20220519T160000Z
UID:TALK174443@talks.cam.ac.uk
DESCRIPTION:Let $G$ be a finite group of Lie type. The work of Deligne-Lus
 ztig (1976) and Lusztig (1984\, 1988) gives rise to the classification of 
 (ordinary) irreducible representations of $G$. While this includes\, in pa
 rticular\, the degrees of the irreducible characters of $G$\, the underlyi
 ng tools do not seem to be sufficient to determine the character table of 
 $G$. To tackle the latter problem\, Lusztig developed the theory of charac
 ter sheaves\, which provides a basis for the space of class functions on $
 G$ that is in principle computable. Thus\, the task is to find the base ch
 ange between this basis and the one consisting of irreducible characters. 
 Due to results of Lusztig and Shoji\, this problem is in many cases essent
 ially reduced to determining certain scalars. We report on some recent pro
 gress in this area.
LOCATION:Seminar Room 2\, Newton Institute
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