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Characters and character sheaves of finite groups of Lie type

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GRA2 - Groups, representations and applications: new perspectives

Let $G$ be a finite group of Lie type. The work of Deligne-Lusztig (1976) and Lusztig (1984, 1988) gives rise to the classification of (ordinary) irreducible representations of $G$. While this includes, in particular, the degrees of the irreducible characters of $G$, the underlying tools do not seem to be sufficient to determine the character table of $G$. To tackle the latter problem, Lusztig developed the theory of character 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 change between this basis and the one consisting of irreducible characters. Due to results of Lusztig and Shoji, this problem is in many cases essentially reduced to determining certain scalars. We report on some recent progress in this area.

This talk is part of the Isaac Newton Institute Seminar Series series.

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