The duality operation in the character ring of a finite Chevalley group

Dean Alvis

Type: Article

Publication Date: 1979-01-01

Citations: 49

DOI: https://doi.org/10.1090/s0273-0979-1979-14690-1

Abstract

It is possible (as in [4] ) to define a duality operation f -• f * in the ring of virtual characters of an arbitrary finite group with a split (B, 7V)-pair of characteristic p.Such a group arises as the fixed points under a Frobenius map of a connected reductive algebraic group, defined over a finite field [1].This paper contains statements of several general properties of the duality map f -• f * and two related operations (see § §2 and 4).The duality map f -• f * generalizes the construction in [2] of the Steinberg character, and interacts well with the organization of the characters from the point of view of cuspidal characters ( §6).It is hoped that there is also a useful interaction with the Deligne-Lusztig virtual characters R^O.Partial results have been obtained in this direction ( §5).Detailed proofs will appear elsewhere.

Locations

Project Euclid (Cornell University) - View - PDF
Bulletin of the American Mathematical Society - View - PDF

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