A Quiver Presentation for Solomon's Descent Algebra
| dc.creator | Pfeiffer, Goetz | |
| dc.date | 2007-09-25 | |
| dc.date | 2008-11-06 | |
| dc.date.accessioned | 2026-07-07T10:15:31Z | |
| dc.date.available | 2026-07-07T10:15:31Z | |
| dc.description | The descent algebra $Σ(W)$ is a subalgebra of the group algebra $\Q W$ of a finite Coxeter group $W$, which supports a homomorphism with nilpotent kernel and commutative image in the character ring of $W$. Thus $Σ(W)$ is a basic algebra, and as such it has a presentation as a quiver with relations. Here we construct $Σ(W)$ as a quotient of a subalgebra of the path algebra of the Hasse diagram of the Boolean lattice of all subsets of $S$, the set of simple reflections in $W$. From this construction we obtain some general information about the quiver of $Σ(W)$ and an algorithm for the construction of a quiver presentation for the descent algebra $Σ(W)$ of any given finite Coxeter group $W$. | |
| dc.description | 45 pages, 5 figures. v3: corrected typos, updated references; to appear in Adv. Math | |
| dc.identifier | https://arxiv.org/abs/0709.3914 | |
| dc.identifier | http://arxiv.org/abs/0709.3914 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173198 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20F55; 20F05; 20C40 | |
| dc.title | A Quiver Presentation for Solomon's Descent Algebra | |
| dc.type | text |