Exceptional representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras
| dc.creator | Jensen, Bernt Tore | |
| dc.creator | Su, Xiuping | |
| dc.creator | Yu, Rupert W. T. | |
| dc.date | 2007-07-24 | |
| dc.date.accessioned | 2026-07-07T08:19:58Z | |
| dc.date.available | 2026-07-07T08:19:58Z | |
| dc.description | In this paper, we study the set of $Δ$-filtered modules of quasi-hereditary algebras arising from quotients of the double of quivers of type $A$. Our main result is that for any fixed $Δ$-dimension vector, there is a unique (up to isomorphism) exceptional $Δ$-filtered module. We then apply this result to show that there is always an open adjoint orbit in the nilpotent radical of a seaweed Lie algebra in $\mathrm{gl}_{n}(\field)$, thus answering positively in this $\mathrm{gl}_{n}(\field)$ case to a question raised independently by Michel Duflo and Dmitri Panyushev. An example of a seaweed Lie algebra in a simple Lie algebra of type $E_{8}$ not admitting an open orbit in its nilpotent radical is given. | |
| dc.identifier | https://arxiv.org/abs/0707.3597 | |
| dc.identifier | http://arxiv.org/abs/0707.3597 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134948 | |
| dc.subject | Representation Theory | |
| dc.subject | 16G20, 17B45 | |
| dc.title | Exceptional representations of a double quiver of type A, and Richardson elements in seaweed Lie algebras | |
| dc.type | text |