Work

Generalised hook lengths and Schur elements for Hecke algebras

Year: 2025

Type: article

Abstract: We compare two generalisations of the notion of hook lengths for partitions. We apply this in the context of the modular representation theory of Arike–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.

Source: Algebraic Combinatorics

DOI: 10.5802/alco.438

Authors: Maria Chlouveraki, Jean-Baptiste Gramain, Nicolas Jacon

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Agence Nationale de la Recherche, Hellenic Foundation for Research and Innovation

Awards: G5633556641, Symmetrizing and Markov Traces on Algebras

OpenAlex ID: W4413891951