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arXiv · 2208.05711

Schurian-finiteness of blocks of type $A$ Hecke algebras II

Sinéad Lyle·Liron Speyer
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Abstract

For any algebra $A$ over an algebraically closed field $\mathbb{F}$, we say that an $A$-module $M$ is Schurian if $\mathrm{End}_A(M) \cong \mathbb{F}$. We say that $A$ is Schurian-finite if there are only finitely many isomorphism classes of Schurian $A$-modules, and Schurian-infinite otherwise. In this paper, we build on the work of Ariki and the second author to show that all blocks of type $A$ Hecke algebras of weight at least $2$ in quantum characteristic $e \geq 3$ are Schurian-infinite. This proves that if $e \geq 3$ then blocks of type $A$ Hecke algebras are Schurian-finite if and only if they are representation-finite.

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Sinéad Lyle, Liron Speyer. 2022-08-11. Schurian-finiteness of blocks of type $A$ Hecke algebras II. https://arxiv.org/abs/2208.05711

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