Modular Lie powers and the Solomon descent algebra
| dc.creator | Erdmann, Karin | |
| dc.creator | Schocker, Manfred | |
| dc.date | 2004-08-16 | |
| dc.date.accessioned | 2026-07-07T05:11:18Z | |
| dc.date.available | 2026-07-07T05:11:18Z | |
| dc.description | Let $V$ be an $r$-dimensional vector space over an infinite field $F$ of prime characteristic $p$, and let $L_n(V)$ denote the $n$-th homogeneous component of the free Lie algebra on $V$. We study the structure of $L_n(V)$ as a module for the general linear group $GL_r(F)$ when $n=pk$ and $k$ is not divisible by $p$ and where $n \geq r$. Our main result is an explicit 1-1 correspondence, multiplicity-preserving, between the indecomposable direct summands of $L_k(V)$ and the indecomposable direct summands of $L_n(V)$ which are not isomorphic to direct summands of $V^{\otimes n}$. The direct summands of $L_k(V)$ have been parametrised earlier, by Donkin and Erdmann. Bryant and Stöhr have considered the case $n=p$ but from a different perspective. Our approach uses idempotents of the Solomon descent algebras, and in addition a correspondence theorem for permutation modules of symmetric groups. | |
| dc.identifier | https://arxiv.org/abs/math/0408211 | |
| dc.identifier | http://arxiv.org/abs/math/0408211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72195 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 17B60 (primary), 17B01, 20C20, 20C30, 05E99 (secondary) | |
| dc.title | Modular Lie powers and the Solomon descent algebra | |
| dc.type | text |