Degree divisibility in Alperin-McKay correspondences
Representation Theory
2022-12-16 v3 Group Theory
Abstract
Let p be a prime, B a p-block of a finite group G and b its Brauer correspondent. According to the Alperin-McKay Conjecture, there exists a bijection between the set of irreducible ordinary characters of height zero of B and those of b. In this paper, we show that whenever G is p-solvable such a bijection can be found, both for ordinary and Brauer characters, with the additional property of being compatible with divisibility of character degrees. In this case, we also show that the dimension of b divides the dimension of B.
Keywords
Cite
@article{arxiv.2204.10124,
title = {Degree divisibility in Alperin-McKay correspondences},
author = {J. Miquel Martìnez and Damiano Rossi},
journal= {arXiv preprint arXiv:2204.10124},
year = {2022}
}
Comments
A mistake was found in an earlier version. It is corrected in the new version. Moreover, further results are proved