2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160827The aim of this paper is to gather and (try to) unify several approaches for the modular representation theory of Hecke algebras of type $B$. We attempt to explain the connections between Geck's cellular structures (coming from Kazhdan-Lusztig theory with unequal parameters) and Ariki's Theorem on the canonical basis of the Fock spaces.Representation TheoryCombinatorics20C08; 20C05; 05E15text