The McKay conjecture and Galois automorphisms
Annals of mathematics, Tome 160 (2004) no. 3, pp. 1129-1140
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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.
@article{10_4007_annals_2004_160_1129,
author = {Gabriel Navarro},
title = {The {McKay} conjecture and {Galois} automorphisms},
journal = {Annals of mathematics},
pages = {1129--1140},
publisher = {mathdoc},
volume = {160},
number = {3},
year = {2004},
doi = {10.4007/annals.2004.160.1129},
mrnumber = {2144975},
zbl = {1079.20010},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2004.160.1129/}
}
TY - JOUR AU - Gabriel Navarro TI - The McKay conjecture and Galois automorphisms JO - Annals of mathematics PY - 2004 SP - 1129 EP - 1140 VL - 160 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2004.160.1129/ DO - 10.4007/annals.2004.160.1129 LA - en ID - 10_4007_annals_2004_160_1129 ER -
Gabriel Navarro. The McKay conjecture and Galois automorphisms. Annals of mathematics, Tome 160 (2004) no. 3, pp. 1129-1140. doi: 10.4007/annals.2004.160.1129
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