e-Cores and e-Weights of Multipartitions and Blocks of Ariki-Koike Algebras

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• Kai Meng Tan, National University of Singapore
• Tuesday 28 May 2024, 16:30-17:30
• MR19 (Potter Room, Pavilion B), CMS.

If you have a question about this talk, please contact Adam Jones.

The Uglov map sends a multipartition (with an associated multicharge) to a partition. Using this Uglov map, I will show how one can use the e-abacus to define the e-core (which is a partition) and the e-weight (which is a non-negative integer) of a multipartition associated to a multi-e-residue. This combinatorial definition of $e$-weight coincides with the definition first introduced by Fayers. Furthermore, two Specht modules of an Ariki-Koike algebra lie in the same block if and only if they are labelled by multipartitions with the same e-core and the same e-weight. This thus provides a characterisation of the blocks of Ariki-Koike algebras that is analogous to that of Iwahori-Hecke algebras. If time allows, I will discuss the implications of these results for Scopes’s equivalences for the blocks of Ariki-Koike algebras, as well as suggest a definition of Rouquier blocks of Ariki-Koike algebras that is different from Lyle’s, but is perhaps more natural.

This talk is part of the Algebra and Representation Theory Seminar series.

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