A simple character formula
Annales Henri Lebesgue, Volume 4 (2021), pp. 503-535.

Metadata

Keywords reductive algebraic groups, characters, $p$-canonical basis

Abstract

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.


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