Scopes equivalences for Ariki-Koike algebras

Speaker: Prof. KaiMeng Tan，新加坡国立大学

Inviter: 方明

Title: Scopes equivalences for Ariki-Koike algebras

Language: English

Time & Venue: 2026.07.02  14:30-15:30  南楼N818

Abstract: Scopes equivalence is a powerful tool in the modular representation theory of symmetric groups and Hecke algebras, where it gives explicit Morita equivalences between suitable blocks and leads to finite classification results. In the setting of Ariki-Koike algebras, an analogous theory exists via the affine Weyl group action arising from categorification, but a clean combinatorial description has been much less accessible. In this talk, I will describe the complete classification of Scopes equivalence classes for blocks of Ariki-Koike algebras in terms of three combinatorial invariants: moving vectors, Scopes vectors, and pyramid numbers. This extends the classification for core blocks and generalises earlier level 1 results, giving a uniform description of Scopes classes across all blocks.