The McKay conjecture and Galois automorphisms

• 成果类型: Article
• 署名作者: Navarro, G
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.160.1129
• 发表日期: 2004
• 页码: 1129-1140
• 关键词: cyclic defect-groups; characters; blocks

摘要

The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group G can be computed locally. The simplest of these conjectures is the McKay conjecture which asserts that the number of irreducible complex characters of G of degree not divisible by p is the same if computed in a p-Sylow normalizer of G. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphisms. In fact, the same idea can be applied to the celebrated Alperin and Dade conjectures.