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Permutation modules for the symmetric group

Authors: Clara Franchi, Alexander A. Ivanov and Mario Mainardis
Journal: Proc. Amer. Math. Soc. 145 (2017), 3249-3262
MSC (2010): Primary 20C30, 20C15
Published electronically: January 25, 2017
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Abstract: In this paper we present a general method for computing the irreducible components of the permutation modules of the symmetric groups over a field $ F$ of characteristic 0. We apply this machinery to determine the decomposition into irreducible submodules of the $ F[S_n]$-permutation module on the right cosets of the normaliser in $ S_n$ of the subgroup generated by a permutation of type $ (3,3)$.

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Clara Franchi
Affiliation: Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41 I-25121 Brescia, Italy

Alexander A. Ivanov
Affiliation: Department of Mathematics, Imperial College, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom

Mario Mainardis
Affiliation: Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università degli Studi di Udine, via delle Scienze 206, I-33100 Udine, Italy

Received by editor(s): June 8, 2016
Received by editor(s) in revised form: September 5, 2016
Published electronically: January 25, 2017
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2017 American Mathematical Society

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