Action of automorphisms on irreducible characters of symplectic groups

By Jay Taylor. Journal of Algebra, 2016

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Abstract Assume G is a finite symplectic group Sp 2 n ( q ) over a finite field F q of odd characteristic. We describe the action of the automorphism group Aut ( G ) on the set Irr ( G ) of ordinary irreducible characters of G. This description relies on the equivariance of Deligne–Lusztig induction with respect to automorphisms. We state a version of this equivariance which gives a precise way to compute the automorphism on the corresponding Levi subgroup; this may be of independent interest. As an application we prove that the global condition in Spath's criterion for the inductive McKay condition holds for the irreducible characters of Sp 2 n ( q ) .

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/db5cf1477de5328e496bb31172535f9f35b7f5c3

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