Decomposable Specht modules indexed by bihooks

TL;DR

This paper investigates when Specht modules labeled by bihooks decompose in the Iwahori--Hecke algebra of type B, identifying many decomposable cases and conjecturing a complete classification.

Contribution

It provides a large family classification of decomposable Specht modules indexed by bihooks and proves the conjecture for small n.

Findings

Identified a large family of decomposable Specht modules

Conjectured this family is complete for bihooks

Proved the conjecture for small n

Abstract

We study the decomposability of Specht modules labelled by bihooks, bipartitions with a hook in each component, for the Iwahori--Hecke algebra of type $B$. In all characteristics, we determine a large family of decomposable Specht modules, and conjecture that these provide a complete list of decomposable Specht modules indexed by bihooks. We prove the conjecture for small $n$.