Alvis-Curtis duality, central characters, and real-valued characters

Details Alvis-Curtis duality, central characters, and real-valued characters Alvis-Curtis duality, central characters, and real-valued characters

2008-10-30

arxiv.org/abs/0810.5513v1

Mathematics

Representation Theory

Scientific paper

We prove that Alvis-Curtis duality 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.

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