Ribbon blocks for centraliser algebras of symmetric groups

2025/02/19 by Matthew Fayers, Fayers, Matthew, Lorenzo Putignano +1
Mathematics · #Finite Group Theory Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2502.13867

Abstract

Suppose l,m are natural numbers with l≤ m, and \mathbbF a field of characteristic p, and let C_l,m^\mathbbF denote the centraliser of the group algebra \mathbbFS_l inside \mathbbFS_m. Ellers and Murray give a conjectured classification of the blocks of C_l,m^\mathbbF, in terms of the p-blocks of S_l and S_m. We prove this conjecture for a family of blocks that we call ribbon blocks and belt blocks. These are the blocks containing Specht modules labelled by skew partitions having no repeated entries in their p-content.

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