## Osaka Journal of Mathematics

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

C. Ryan Vinroot

#### 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

https://projecteuclid.org/euclid.ojm/1277298916

Mathematical Reviews number (MathSciNet)
MR2722372

Zentralblatt MATH identifier
1209.20010

#### 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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