2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67609The 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.AmSLaTeX, 9 pages, 15 referencesAlgebraic GeometryRepresentation Theory14L30 (Primary) 20G05, 22E46 (Secondary)text