Complexity of homogeneous spaces and growth of multiplicities

dc.creatorTimashev, Dmitri A.
dc.date2003-05-29
dc.date2003-09-09
dc.date.accessioned2026-07-07T04:58:22Z
dc.date.available2026-07-07T04:58:22Z
dc.descriptionThe 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.descriptionAmSLaTeX, 9 pages, 15 references
dc.identifierhttps://arxiv.org/abs/math/0305416
dc.identifierhttp://arxiv.org/abs/math/0305416
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67609
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14L30 (Primary) 20G05, 22E46 (Secondary)
dc.titleComplexity of homogeneous spaces and growth of multiplicities
dc.typetext

Files

Collections