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Malle, Gunter; Späth, Britta

Characters of odd degree. (English) Zbl 1397.20016

Ann. Math. (2) 184, No. 3, 869-908 (2016).
Summary: 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 \(\ell\) such that a Sylow \(\ell\)-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 most of them lie in the principal Harish-Chandra series, then allow us to deduce from it the McKay conjecture for the prime 2, hence for characters of odd degree.

Cited in 2 Reviews
Cited in 48 Documents

MSC:

20C15 Ordinary representations and characters
20C33 Representations of finite groups of Lie type

Keywords:

characters of odd degree; equivariant Harish-Chandra theory; McKay conjecture
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\textit{G. Malle} and \textit{B. Späth}, Ann. Math. (2) 184, No. 3, 869--908 (2016; Zbl 1397.20016)
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