# 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…
7 Citations
Prime power variations of higher Lien modules
On conjugacy classes of Sn containing all irreducibles
It is shown that for the conjugation action of the symmetric group Sn, when n = 6 or n ≥ 8, all Sn-irreducibles appear as constituents of a single conjugacy class, namely, one indexed by a partition
On a curious variant of the Sn-module Lien
We introduce a variant of the much-studied Lie representation of the symmetric group Sn, which we denote by Lie n . Our variant gives rise to a decomposition of the regular representation as a sum of
The plethystic inverse of the odd Lie representations $Lie_{2n+1}$
The Frobenius characteristic of $Lie_n,$ the representation of the symmetric group $S_n$ afforded by the free Lie algebra, is known to satisfy many interesting plethystic identities. In this paper we
On a curious variant of the $S_n$-module Lie$_n$
We introduce a variant of the much-studied $Lie$ representation of the symmetric group $S_n$, which we denote by $Lie_n^{(2)}.$ Our variant gives rise to a decomposition of the regular representation
Variations on the $S_n$-module $Lie_n$
We define, for each subset $S$ of primes, an $S_n$-module $Lie_n^S$ with interesting properties. When $S=\emptyset,$ this is the well-known representation $Lie_n$ of $S_n$ afforded by the free Lie
On a Positivity Conjecture in the Character Table of Sn
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.

## References

SHOWING 1-10 OF 41 REFERENCES
Some Aspects of Groups Acting on Finite Posets
Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type
• Mathematics
• 2013
Let G be a finite simple group of Lie type, and let πG be the permutation representation of G associated with the action of G on itself by conjugation. We prove that every irreducible complex
On the reduction of the conjugating representation of a finite group
Here we define the group vector y to be a g X l column vector whose entries are the elements of G, arranged so that the identity element 71 is first, and so that the hff elements of a class C9 of
On the Existence of Tableaux with Given Modular Major Index
We provide simple necessary and sufficient conditions for the existence of a standard Young tableau of a given shape and major index $r$ mod $n$, for all $r$. Our result generalizes the $r=1$ case
C O ] 1 1 D ec 2 01 5 REPRESENTATION STABILITY FOR COHOMOLOGY OF CONFIGURATION SPACES IN R
• Mathematics
• 2015
This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group Sn on the cohomology of the configuration space of n ordered points in R. This
Theorem about the conjugacy representation ofSn
Every group has two natural representations on itself, the regular representation and the conjugacy representation. We know everything about the construction of the regular representation, but we
Representation stability for cohomology of configuration spaces in $\mathbf{R}^d$
• Mathematics
• 2015
This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group $S_n$ on the cohomology of the configuration space of $n$ ordered points in
The Representation Theory of the Symmetric Group
• Mathematics
• 2009
1. Symmetric groups and their young subgroups 2. Ordinary irreducible representations and characters of symmetric and alternating groups 3. Ordinary irreducible matrix representations of symmetric
Clifford theory and applications
• Mathematics
• 2008
This is an introduction to Clifford theory of induced representations from normal subgroups of finite groups. As an application, a complete explicit description of the irreducible representations of
Representations of finite and compact groups
Groups and counting principles Fundamentals of group representations Abstract theory of representations of finite groups Representations of concrete finite groups. I: Abelian and Clifford groups