vix.ing · top · new · best · stats · spec

Global sections of line bundles on a wonderful compactification of the general linear group

2003/05/01 by Ivan Kausz, Kausz, Ivan
Mathematics · #14L30 #20G05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14L30 #msc:20G05

paper · pdf · doi:10.48550/arxiv.math/0305033

16 pages. In this new version I review more extensively the results I need from my paper on the compactification of the general linear group

openalex publication_date 2003/05/01 · arxiv created 2004/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a previous paper we have constructed a compactification KGln of the general linear group Gln, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De Concini and Procesi. In particular there is an action of G=Gln× Gln on this compactification. In this paper we show how the space of global section of an arbitrary G-linearized line bundle on KGln decomposes canonically into a direct sum of simple G-modules which are themselves given as the spaces of global sections of line bundles on the product of two copies of the full flag manifold parametrizing flags in an n-dimensional vector space.

Related