Schurian‐finiteness of blocks of type Hecke algebras

For any algebra over an algebraically closed field , we say that an -module is Schurian ifEnd() ≅ . We say that is Schurian-finite if there are only finitely many isomorphism classes of Schurian -modules, and Schurian-infinite otherwise. By work of Demonet, Iyama and Jasso, it is known that Schurian-finiteness is equivalent to -tilting-finiteness, so thatwemay drawon a wealth of known results in the subject. We prove that for the type Hecke algebras with quantum characteristic ⩾ 3, all blocks of weight at least 2 are Schurianinfinite in any characteristic. Weight 0 and 1 blocks are known by results of Erdmann and Nakano to be representation finite, and are therefore Schurian-finite. This means that blocks oftype Hecke algebras (when ⩾ 3) are Schurian-infinite if and only if they have wild representation type if and only if the module category has finitely many wide subcategories. Along theway, we also prove a graded version of the Scopes equivalence, which is likely to be of independent interest.journal articl