A simple character formula

Riche, Simon; Williamson, Geordie

Annales Henri Lebesgue, Tome 4 (2021), pp. 503-535.

Dans cet article nous démontrons une formule de caractères exprimant les classes des représentations simples dans le bloc principal d’un groupe algébrique semi-simple $G$ en termes des modules de Verma bébé, sous l’hypothèse que la caractéristique du corps de base est supérieure à $2h-1$, où $h$ est le nombre de Coxeter de $G$. Ceci fournit un remplacement de la conjecture de Lusztig, valable sous une hypothèse raisonnable sur la caractéristique.

In this paper we prove a character formula expressing the classes of simple representations in the principal block of a simply-connected semisimple algebraic group $G$ in terms of baby Verma modules, under the assumption that the characteristic of the base field is bigger than $2h-1$, where $h$ is the Coxeter number of $G$. This provides a replacement for Lusztig’s conjecture, valid under a reasonable assumption on the characteristic.

Classification : 20G05
Mots clés : reductive algebraic groups, characters, $p$-canonical basis

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