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no. 3
Centraliser algebras of monomial representations and applications in combinatorics
Barrera Acevedo, Santiago1; Ó Catháin, Padraig2; Dietrich, Heiko3; Egan, Ronan4
1 La Trobe University Department of Mathematical and Physical Sciences Bundoora 3083 VIC Australia
2 Dublin City University Fiontar agus Scoil na Gaeilge Drumcondra, Dublin 9 Ireland
3 Monash University School of Mathematics Clayton 3800 VIC Australia
4 Dublin City University School of Mathematical Sciences Glasnevin, Dublin 9 Ireland
Algebraic Combinatorics, Volume 8 (2025) no. 3, pp. 687-710.

Centraliser algebras of monomial representations of finite groups may be constructed and studied using methods similar to those employed in the study of permutation groups. Guided by results of D. G. Higman and others, we give an explicit construction for a basis of the centraliser algebra of a monomial representation. The character table of this algebra is then constructed via character sums over double cosets. We locate the theory of group-developed and cocyclic-developed Hadamard matrices within this framework. We apply Gröbner bases to produce a new classification of highly symmetric complex Hadamard matrices.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.426
Classification: 05B20, 20B25
Keywords: monomial representation, centraliser algebra, complex Hadamard matrix

Barrera Acevedo, Santiago 1; Ó Catháin, Padraig 2; Dietrich, Heiko 3; Egan, Ronan 4

1 La Trobe University Department of Mathematical and Physical Sciences Bundoora 3083 VIC Australia
2 Dublin City University Fiontar agus Scoil na Gaeilge Drumcondra, Dublin 9 Ireland
3 Monash University School of Mathematics Clayton 3800 VIC Australia
4 Dublin City University School of Mathematical Sciences Glasnevin, Dublin 9 Ireland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Barrera Acevedo, Santiago; Ó Catháin, Padraig; Dietrich, Heiko; Egan, Ronan. Centraliser algebras of monomial representations and applications in combinatorics. Algebraic Combinatorics, Volume 8 (2025) no. 3, pp. 687-710. doi : 10.5802/alco.426. https://alco.centre-mersenne.org/articles/10.5802/alco.426/

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