Alvis-Curtis duality, central characters, and real-valued characters
Representation Theory
2008-10-31 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0810.5513,
title = {Alvis-Curtis duality, central characters, and real-valued characters},
author = {C. Ryan Vinroot},
journal= {arXiv preprint arXiv:0810.5513},
year = {2008}
}