Specht modules labelled by hook bipartitions II

TL;DR

This paper advances the understanding of Specht modules labeled by hook bipartitions for type B Iwahori--Hecke algebras, providing explicit graded decomposition matrices over arbitrary fields.

Contribution

It explicitly determines the graded decomposition submatrices for Specht modules labeled by hook bipartitions in the cyclotomic Khovanov--Lauda--Rouquier algebra setting.

Findings

Explicit graded decomposition matrices are obtained.

Results apply over arbitrary fields.

Focus on modules labeled by hook bipartitions in type B.

Abstract

We continue the study of Specht modules labelled by hook bipartitions for the Iwahori--Hecke algebra of type $B$ with $e\in\{3,4,\dots\}$ via the cyclotomic Khovanov--Lauda--Rouquier algebra $\mathscr{H}_n^{\Lambda}$. Over an arbitrary field, we explicitly determine the graded decomposition submatrices for $\mathscr{H}_n^{\Lambda}$ comprising rows corresponding to hook bipartitions.