The conjugacy action of $$S_n$$Sn and modules induced from centralisers

@article{Sundaram2016TheCA,
  title={The conjugacy action of \$\$S\_n\$\$Sn and modules induced from centralisers},
  author={S. Sundaram},
  journal={Journal of Algebraic Combinatorics},
  year={2016},
  volume={48},
  pages={179-225}
}
  • S. Sundaram
  • Published 18 March 2016
  • Mathematics
  • Journal of Algebraic Combinatorics
We establish, for the character table of the symmetric group, the positivity of the row sums indexed by irreducible characters, when restricted to various subsets of the conjugacy classes. A notable example is that of partitions with all parts odd. More generally, we study representations related to the conjugacy action of the symmetric group. These arise as sums of submodules induced from centraliser subgroups, and their Frobenius characteristics have elegant descriptions, often as a… 
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Methods Citations
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7 Citations

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Prime power variations of higher Lien modules
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TLDR
This work investigates the conjecture that the sum of power sums for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive and establishes its truth in the following special cases.

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