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Alperin weight bijections and dimensions of simple modules
Abstract
We propose a new refinement of the (blockwise) Alperin weight conjecture taking dimensions of simple modules (or degrees of irreducible Brauer characters) into consideration. This is similar to Giannelli's refinement of the (Alperin--)McKay conjecture. We prove this new refinement for blocks with a cyclic or Klein four defect group, for inertial blocks (which include the Broué--Puig nilpotent blocks), and for p-blocks of p-solvable groups.
Related
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BibTeX
@misc{huang2026alperin,
title = {{Alperin weight bijections and dimensions of simple modules}},
author = {Xin Huang and Hanxiao Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05271},
eprint = {2611.05271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05271},
}
RIS
TY - UNPB
TI - Alperin weight bijections and dimensions of simple modules
AU - Xin Huang
AU - Hanxiao Li
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05271
UR - https://arxiv.org/abs/2611.05271
AB - We propose a new refinement of the (blockwise) Alperin weight conjecture taking dimensions of simple modules (or degrees of irreducible Brauer characters) into consideration. This is similar to Giannelli's refinement of the (Alperin--)McKay conjecture. We prove this new refinement for blocks with a cyclic or Klein four defect group, for inertial blocks (which include the Broué--Puig nilpotent blocks), and for p-blocks of p-solvable groups.
ER -