Characters of odd degree

2015/06/25 by Gunter Malle, Malle, Gunter, Britta Späth +1 · 4 citations
Mathematics · #20C08 #20C15 #20C33 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C08 #msc:20C15 #msc:20C33

paper · pdf · doi:10.48550/arxiv.1506.07690

arxiv created 2015/06/25 · arxiv updated 2015/06/26

Abstract

We prove the McKay conjecture on characters of odd degree. A major step in the proof is the verification of the inductive McKay condition for groups of Lie type and primes ℓ such that a Sylow ℓ-subgroup or its maximal normal abelian subgroup is contained in a maximally split torus by means of a new equivariant version of Harish-Chandra induction. Specifics of characters of odd degree, namely that they only lie in very particular Harish-Chandra series then allow us to deduce from it the McKay conjecture for the prime~2, hence for characters of odd degree.

Cited by

• The McKay conjecture with coprime group automorphisms and the Okuyama-Wajima argument
• The Picky Conjecture for groups of Lie type
• McKay bijections and character degrees
• Generic weights for finite reductive groups

Related

• New refinements of the McKay conjecture for arbitrary finite groups
• The McKay Conjecture on character degrees
• McKay bijections and character degrees
• Equivariant character correspondences and inductive McKay condition for type A
• Odd Character Degrees for Sp(2n,2)