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no. 4
Generalised hook lengths and Schur elements for Hecke algebras
Chlouveraki, Maria1; Gramain, Jean-Baptiste2; Jacon, Nicolas3
1 National and Kapodistrian University of Athens Department of Mathematics Panepistimioupolis 15784 Athens Greece
2 Institute of Mathematics University of Aberdeen King’s College Fraser Noble Building Aberdeen AB24 3UE UK
3 Université de Reims Champagne-Ardennes UFR Sciences exactes et naturelles Laboratoire de Mathématiques UMR CNRS 9008 Moulin de la Housse BP 1039 51100 REIMS France
Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 1069-1084.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.438
Classification: 05E10, 20C08, 20C20
Keywords: hook lengths, Schur elements, Hecke algebras

Chlouveraki, Maria 1; Gramain, Jean-Baptiste 2; Jacon, Nicolas 3

1 National and Kapodistrian University of Athens Department of Mathematics Panepistimioupolis 15784 Athens Greece
2 Institute of Mathematics University of Aberdeen King’s College Fraser Noble Building Aberdeen AB24 3UE UK
3 Université de Reims Champagne-Ardennes UFR Sciences exactes et naturelles Laboratoire de Mathématiques UMR CNRS 9008 Moulin de la Housse BP 1039 51100 REIMS France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Chlouveraki, Maria; Gramain, Jean-Baptiste; Jacon, Nicolas. Generalised hook lengths and Schur elements for Hecke algebras. Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 1069-1084. doi : 10.5802/alco.438. https://alco.centre-mersenne.org/articles/10.5802/alco.438/

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