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arXiv · 2302.12129

Descent of splendid Rickard equivalences in ${\rm GL}_n(q)$

Xin Huang·Pengcheng Li·Jiping Zhang
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Abstract

Let $n$ be a positive integer and $q$ a prime power. We prove that a refined version of Brou\'{e}'s abelian defect group conjecture holds for unipotent $\ell$-blocks of ${\rm GL}_n(q)$, where $\ell\nmid q$. We also give a sufficient condition on general $\ell$-blocks of ${\rm GL}_n(q)$ to satisfy the refined abelian defect group conjecture. We explain by an example that this sufficient condition does not hold in general.

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BibTeXRIS

Xin Huang, Pengcheng Li, Jiping Zhang. 2023-02-23. Descent of splendid Rickard equivalences in ${\rm GL}_n(q)$. https://doi.org/10.1016/j.jpaa.2024.107711

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