On conjugacy classes of S n containing all irreducibles
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It is shown that for the conjugation action of the symmetric group S n , when n = 6 or n ≥ 8, all S n -irreducibles appear as constituents of a single conjugacy class, namely, one indexed by a partition λ of n with at least two parts, whose parts are all distinct and taken from the set of odd primes and 1. A simple characterisation of conjugacy classes containing all irreducibles is proved.
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- S. Sundaram, The conjugacy action of Sn and submodules induced from centralisers, Journal of Algebraic Combinatorics, to appear, https://doi.org/10.1007/s10801-017-0796-9.Google Scholar
- J. Swanson, On the existence of tableaux with given major modular index, Algebraic Combinatorics, to appear, arXiv:1701.04936.Google Scholar