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Rationality Questions for Finite Reductive Groups

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GR2W01 - Counting conjectures and beyond

Each (complex) irreducible character of a finite group determines a subfield of the complex numbers called its character field. This is the smallest subfield containing all character values. One can then ask whether there exists a representation of the group affording the character all of whose matrix entries are contained in the character field. Such a representation need not exist in general and the failure of such a representation to exist is measured by the Schur index. In this talk we will discuss results around character fields and Schur indices in the case where the group is a finite reductive group.

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

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