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)$.
Franchi, C., Ivanov, A. A., Mainardis, M., Permutation modules for the symmetric group, <<PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY>>, 2017; 145 (Number 8, August): 3249-3262. [doi:10.1090/proc/13474] [http://hdl.handle.net/10807/102133]
Permutation modules for the symmetric group
Franchi, ClaraPrimo
;
2017
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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