Geodesic
Action of the Symmetric Group on the Free LAnKe: a CataLAnKe Theorem
Séminaire lotharingien de combinatoire, 80B (2018)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We initiate a study of the representation of the symmetric group on the multilinear component of an n-ary generalization of the free Lie algebra, which we call a free LAnKe. Our central result is that the representation of the symmetric group S2n-1 on the multilinear component of the free LAnKe with 2n-1 generators is given by an irreducible representation whose dimension is the nth Catalan number. This leads to a more general result on eigenspaces of a certain linear operator. A decomposition, into irreducibles, of the representation of S3n-2 on the multilinear component the free LAnKe with 3n-2 generators is also presented. We also obtain a new presentation of Specht modules of shape λ, where λ has strictly decreasing column lengths, as a consequence of our eigenspace result. 

@article{SLC_2018_80B_a62,
     author = {Tamar Friedmann and Philip Hanlon and Richard P. Stanley, and Michelle L. Wachs},
     title = {Action of the {Symmetric} {Group} on the {Free} {LAnKe:} a {CataLAnKe} {Theorem}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a62/}
}
TY  - JOUR
AU  - Tamar Friedmann
AU  - Philip Hanlon
AU  - Richard P. Stanley,
AU  - Michelle L. Wachs
TI  - Action of the Symmetric Group on the Free LAnKe: a CataLAnKe Theorem
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a62/
ID  - SLC_2018_80B_a62
ER  - 
%0 Journal Article
%A Tamar Friedmann
%A Philip Hanlon
%A Richard P. Stanley,
%A Michelle L. Wachs
%T Action of the Symmetric Group on the Free LAnKe: a CataLAnKe Theorem
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a62/
%F SLC_2018_80B_a62
Tamar Friedmann; Philip Hanlon; Richard P. Stanley,; Michelle L. Wachs. Action of the Symmetric Group on the Free LAnKe: a CataLAnKe Theorem. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a62/