Schurian-finiteness conjecture for integral type B Hecke algebra blocks

Let $e$ be the quantum characteristic, let $\hhh$ be an integral type B Hecke algebra, and let $B$ be a block of $\hhh$ with defect at least $2$. Schurian-finiteness conjecture. If $e\geq 4$, then $B$ is Schurian-infinite in any characteristic. In particular, $B$ is Schurian-finite if and only if it has finite representation type.

The conjecture concerns the classification of Schurian-finite blocks for integral Hecke algebras. The paper proves the assertion except for certain blocks of defects $3$ and $4$, so the conjecture remains open in those cases.