Characters of odd degree Characters of odd degree

• 成果类型: Article
• 署名作者: Malle, Gunter; Spaeth, Britta
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.184.3.6
• 发表日期: 2016
• 页码: 869-908
• 关键词: inductive mckay condition; harish-chandra induction; reductive groups; irreducible representations; finite-groups; lie type; conjecture; ELEMENTS; THEOREM

摘要

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 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 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.