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arXiv · 2611.05271

Alperin weight bijections and dimensions of simple modules

Xin Huang·Hanxiao Li
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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.

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Xin Huang, Hanxiao Li. 2026-11-03. Alperin weight bijections and dimensions of simple modules. https://arxiv.org/abs/2611.05271

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