C. Ryan Vinroot
Published 2008-10-30Version 1
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.
On Harish-Chandra series of finite unitary groups and the $\mathfrak{sl}_\infty$-crystal on level $2$ Fock spaces
Harish-Chandra series in finite unitary groups and crystal graphs
Branching graphs for finite unitary groups in non-defining characteristic
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