Category of sp(2n)-modules with bounded weight multiplicities
| dc.creator | Grantcharov, Dimitar | |
| dc.creator | Serganova, Vera | |
| dc.date | 2005-10-03 | |
| dc.date.accessioned | 2026-07-07T06:26:46Z | |
| dc.date.available | 2026-07-07T06:26:46Z | |
| dc.description | Let $g$ be a finite dimensional simple Lie algebra. Denote by $\mathcal B$ the category of all bounded weight $g$-modules, i.e. those which are direct sum of their weight spaces and have uniformly bounded weight multiplicities. A result of Fernando shows that infinite-dimensional bounded weight modules exist only for $g=sl(n)$ and $g=sp(2n)$. If $g=sp(2n)$ we show that $\mathcal B$ has enough projectives if and only if $n>1$. In addition, the indecomposable projective modules can be parameterized and described explicitly. All indecomposable objects are described in terms of indecomposable representations of a certain quiver with relations. This quiver is wild for $n>2$. For $n=2$ we describe all indecomposables by relating the blocks of $\mathcal B$ to the representations of the affine quiver $A_3^{(1)}$. | |
| dc.description | 17 pages, 3 diagrams, 1 figure. Requires the package "diagrams" | |
| dc.identifier | https://arxiv.org/abs/math/0510058 | |
| dc.identifier | http://arxiv.org/abs/math/0510058 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97210 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10 (Primary) 16G60 (Secondary) | |
| dc.title | Category of sp(2n)-modules with bounded weight multiplicities | |
| dc.type | text |