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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 \(\textrm{End}_A(M)\) 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.