2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119500In this paper we study the sections of the canonical line bundle on the moduli space of parabolic semistable vector bundles with trivial determinant and fixed parabolic structure of type $\underlineλ=(λ_1,..., λ_s)$ (with each weight $λ_i$ in $P_{\ell}(\SL(r))$) on a smooth projective irreducible curve over $\C$ of genus $g \geq 1$. We give a nontrivial lower bound for the dimension of the sections (that are called generalized parabolic SL(r)-theta functions) when $\sum_{1}^{s} λ_i$ is in the root lattice.11 pagesAlgebraic GeometryRepresentation Theory14H60; 22E65text