• Corpus ID: 221695098

On a curious variant of the Sn-module Lien

@inproceedings{Sundaram2020OnAC,
  title={On a curious variant of the Sn-module Lien},
  author={S. Sundaram},
  year={2020}
}
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 exterior powers of the modules Lie n . This is in contrast to the theorems of Poincaré–Birkhoff–Witt and Thrall which decompose the regular representation into a sum of symmetrised Lie modules. We show that nearly every known property of Lien has a counterpart for the module Lie n , suggesting… 
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References

SHOWING 1-10 OF 26 REFERENCES
The conjugacy action of $$S_n$$Sn and modules induced from centralisers
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…
A hodge-type decomposition for commutative algebra cohomology
The Integral Tree Representation of the Symmetric Group
AbstractLet Tn be the space of fully-grown n-trees and let Vn and Vn′ be the representations of the symmetric groups Σn and Σn+1 respectively on the unique non-vanishing reduced integral homology…
A Hodge decomposition for the complex of injective words
llReiner and Webb (preprint, 2002) compute the S n -module structure for the complex of injective words. This paper refines their formula by providing a Hodge type decomposition. Along the way, this…
Group actions on arrangements of linear subspaces and applications to configuration spaces
For an arrangement of linear subspaces in RI that is invariant under a finite subgroup of the general linear group Gin(IR) we develop a formula for the G-module structure of the cohomology of the…
The combinatorics of the bar resolution in group cohomology
On the Poincaré Series Associated with Coxeter Group Actions on Complements of Hyperplanes
Let W be a finite Coxeter group, realized as a group generated by reflections in the /-dimensional Euclidean space V. Let s/ be the hyperplane arrangement in C* = F(g)RC consisting of the…
Polynomial Splitting Measures and Cohomology of the Pure Braid Group
We study for each n a one-parameter family of complex-valued measures on the symmetric group $$S_n$$Sn, which interpolate the probability of a monic, degree n, square-free polynomial in $$\mathbb…
Free Lie algebras
My principal references are [Serre:1965], [Reutenauer:1993], and [de Graaf:2000]. My interest in free Lie algebras has been motivated by the well known conjecture that Kac-Moody algebras can be…
The tree representation of ∑n + 1
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