Cellular structures on Hecke algebras of type B

TL;DR

This paper unifies various approaches to the modular representation theory of type B Hecke algebras, linking cellular structures from Kazhdan-Lusztig theory with Ariki's theorem on Fock space bases.

Contribution

It provides a comprehensive framework connecting cellular structures and canonical bases in the context of type B Hecke algebras.

Findings

Unified perspective on cellular structures and canonical bases.

Clarified connections between Kazhdan-Lusztig theory and Ariki's theorem.

Enhanced understanding of modular representations of type B Hecke algebras.

Abstract

The 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.