Complexity of homogeneous spaces and growth of multiplicities
| dc.creator | Timashev, Dmitri A. | |
| dc.date | 2003-05-29 | |
| dc.date | 2003-09-09 | |
| dc.date.accessioned | 2026-07-07T04:58:22Z | |
| dc.date.available | 2026-07-07T04:58:22Z | |
| dc.description | The complexity of a homogeneous space $G/H$ under a reductive group $G$ is by definition the codimension of generic orbits in $G/H$ of a Borel subgroup $B\subseteq G$. We give a representation-theoretic interpretation of this number as the exponent of growth for multiplicities of simple $G$-modules in the spaces of sections of line bundles on $G/H$. For this, we show that these multiplicities are bounded from above by the dimensions of certain Demazure modules. This estimate for multiplicities is uniform, i.e., it depends not on $G/H$, but only on its complexity. | |
| dc.description | AmSLaTeX, 9 pages, 15 references | |
| dc.identifier | https://arxiv.org/abs/math/0305416 | |
| dc.identifier | http://arxiv.org/abs/math/0305416 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67609 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 14L30 (Primary) 20G05, 22E46 (Secondary) | |
| dc.title | Complexity of homogeneous spaces and growth of multiplicities | |
| dc.type | text |