Osaka Journal of Mathematics

Duality, central characters, and real-valued characters of finite groups of Lie type

C. Ryan Vinroot

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Abstract

We prove that the duality operator preserves the Frobenius--Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius--Schur indicator of a regular real-valued character to its central character. We apply these results to compute the Frobenius--Schur indicators of certain real-valued, irreducible, Frobenius-invariant Deligne--Lusztig characters, and the Frobenius--Schur indicators of real-valued regular and semisimple characters of finite unitary groups.

Article information

Source
Osaka J. Math., Volume 47, Number 2 (2010), 523-534.

Dates
First available in Project Euclid: 23 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1277298916

Mathematical Reviews number (MathSciNet)
MR2722372

Zentralblatt MATH identifier
1209.20010

Subjects
Primary: 20C33: Representations of finite groups of Lie type 20G05: Representation theory

Citation

Vinroot, C. Ryan. Duality, central characters, and real-valued characters of finite groups of Lie type. Osaka J. Math. 47 (2010), no. 2, 523--534. https://projecteuclid.org/euclid.ojm/1277298916


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