Schurian-finiteness of blocks of type A Hecke algebras II

2022/08/11 by Sinéad Lyle, Lyle, Sinéad, Liron Speyer +1
Mathematics · #16G10 #20C08 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2208.05711

openalex publication_date 2022/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any algebra A over an algebraically closed field \mathbbF, we say that an A-module M is Schurian if End_A(M) ≅ \mathbbF. 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 ≥ 3 are Schurian-infinite. This proves that if e ≥ 3 then blocks of type A Hecke algebras are Schurian-finite if and only if they are representation-finite.

Related

• Schurian-finiteness of blocks of type B Hecke algebras
• Wild blocks of type A Hecke algebras are strictly wild
• The (Q,q)-Schur algebra
• On q-Schur algebras corresponding to Hecke algebras of type B
• Asymptotic Schur algebras and cellularity of q-Schur algebras