2024/06/27 by Maria Chlouveraki, Chlouveraki, Maria, Jean-Baptiste Gramain +3
Mathematics · #05E10 #20C08 #20C20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2406.19313
openalex publication_date 2024/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compare two generalisations of the notion of hook lengths for partitions. We apply this in the context of the modular representation theory of Ariki-Koike algebras. We show that the Schur element of a simple module is divisible by the Schur element of the associated (generalised) core. In the case of Hecke algebras of type A, we obtain an even stronger result: the Schur element of a simple module is equal to the product of the Schur element of its core and the Schur element of its quotient.