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arXiv · 2608.11568

Scopes equivalence for blocks of Ariki-Koike algebras

Joseph Chuang·Kai Meng Tan
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Abstract

We obtain necessary and sufficient conditions for a block of an Ariki-Koike algebra to have the property that all its associated multipartitions have no addable node with a given residue. This leads to a classification of Scopes equivalence classes for Ariki-Koike algebras in terms of their pyramid numbers and Scopes vectors, generalising that for level 1 and for core blocks. Our proof is independent of the results of Richards for level 1.

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BibTeXRIS

Joseph Chuang, Kai Meng Tan. 2026-08-12. Scopes equivalence for blocks of Ariki-Koike algebras. https://arxiv.org/abs/2608.11568

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