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University of Sydney Algebra Seminar

Liron Speyer

Friday 23 February, 12-1pm, Place: Carslaw 175

Schurian-infinite blocks of type $A$ Hecke algebras

For any algebra $A$ over an algebraically closed field $F$, we say that an $A$-module $M$ is Schurian if ${\text{End}}_A(M)$ is isomorphic to $F$. We say that $A$ is Schurian-finite if there are only finitely many isomorphism classes of Schurian $A$-modules, and Schurian-infinite otherwise. I will present joint work with Susumu Ariki and Sinéad Lyle in which we classified the Schurian-finiteness of blocks of type $A$ Hecke algebras – when $e\ne 2$, a block of the Hecke algebra is Schurian-finite if and only if it has finite representation type, if and only it has weight 0 or 1. I will give an overview of the techniques that were used in this project.