Permutation modules for the symmetric group

Clara Franchi; Alexander A. Ivanov; Mario Mainardis

doi:https://doi.org/10.1090/proc/13474

Permutation modules for the symmetric group

Clara Franchi, Alexander A. Ivanov, Mario Mainardis

Research output: Contribution to journal › Article › peer-review

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)$.

Original language	English
Pages (from-to)	3249-3262
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	145
DOIs	https://doi.org/10.1090/proc/13474
Publication status	Published - 2017

Keywords

Permutation module
Symmetric group

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https://doi.org/10.1090/proc/13474

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title = "Permutation modules for the symmetric group",

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)$.",

keywords = "Permutation module, Symmetric group, Permutation module, Symmetric group",

author = "Clara Franchi and Ivanov, {Alexander A.} and Mario Mainardis",

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publisher = "American Mathematical Society:PO Box 6248:Providence, RI 02940:(800)321-4267, (401)455-4000, EMAIL: cust-serv@ams.org, gma@math.ams.org, INTERNET: http://www.ams.org, Fax: (401)331-3842",

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TY - JOUR

T1 - Permutation modules for the symmetric group

AU - Franchi, Clara

AU - Ivanov, Alexander A.

AU - Mainardis, Mario

PY - 2017

Y1 - 2017

N2 - 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)$.

AB - 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)$.

KW - Permutation module

KW - Symmetric group

KW - Permutation module

KW - Symmetric group

UR - http://hdl.handle.net/10807/102133

U2 - https://doi.org/10.1090/proc/13474

DO - https://doi.org/10.1090/proc/13474

M3 - Article

VL - 145

SP - 3249

EP - 3262

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -

Permutation modules for the symmetric group

Abstract

Keywords

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