Geodesic
The integral tree representation of the symmetric group
Journal of Algebraic Combinatorics, Tome 13 (2001) no. 3, pp. 317-326.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $T _{n}$ be the space of fully-grown $n$-trees and let $V _{n}$ and $V _{n} ^{ \mathbb Z S \_{ n + 1} \mathbb{Z}\Sigma _{n + 1} -modules, giving a description of V $_n ^${ prime} in terms of V $_n$ and V $_ n+1$. This short exact sequence may also be deduced from work of Sundaram. Modulo a twist by the sign representation, V $_n$ is shown to be dual to the Lie representation of $Sgr_ n $, Lie $_ n $. Therefore we have an explicit combinatorial description of the integral representation of $Sgr_ n+1$ on Lie $_ n $ and this representation fits into a short exact sequence involving Lie $_ n $ and Lie $_ n+1$.$
Keywords: symmetric group representation, free Lie algebra 
@article{JAC_2001__13_3_a0,
     author = {Whitehouse, Sarah},
     title = {The integral tree representation of the symmetric group},
     journal = {Journal of Algebraic Combinatorics},
     pages = {317--326},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2001__13_3_a0/}
}
TY  - JOUR
AU  - Whitehouse, Sarah
TI  - The integral tree representation of the symmetric group
JO  - Journal of Algebraic Combinatorics
PY  - 2001
SP  - 317
EP  - 326
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2001__13_3_a0/
LA  - en
ID  - JAC_2001__13_3_a0
ER  - 
%0 Journal Article
%A Whitehouse, Sarah
%T The integral tree representation of the symmetric group
%J Journal of Algebraic Combinatorics
%D 2001
%P 317-326
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2001__13_3_a0/
%G en
%F JAC_2001__13_3_a0
Whitehouse, Sarah. The integral tree representation of the symmetric group. Journal of Algebraic Combinatorics, Tome 13 (2001) no. 3, pp. 317-326. http://geodesic.mathdoc.fr/item/JAC_2001__13_3_a0/