On decomposition numbers and Alvis-Curtis duality
classification
🧮 math.RT
keywords
alvis-curtisdecompositiondualityknowledgenumbersalgebrascharacteristicequivalent
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We show that for general linear groups ${\rm GL}_n(q)$ as well as for $q$-Schur algebras the knowledge of the modular Alvis-Curtis duality over fields of characteristic $\ell$, $\ell \nmid q$, is equivalent to the knowledge of the decomposition numbers.
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