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

Equivariant vector bundles on group completions

2002/02/28 by Syu Kato · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #math.AG #math.RT #msc:14F05 #msc:14J60 #msc:14M17 #msc:18F99

paper · pdf · doi:10.1515/crll.2005.2005.581.71

published as J. reine angew. Math. 581 (2005) 71-116 · Final version. Improved Exposition. to appear in Crelle's J. 43pages

arxiv created 2004/03/31 · openalex publication_date 2005/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

In this paper, we describe the category of bi-equivariant vector bundles on a bi-equivariant smooth (partial) compactification of a connected reductive algebraic group with normal crossing boundary divisors. Our result is a generalization of the description of the category of equivariant vector bundles on toric varieties established by A. A. Klyachko (Math. USSR Izvest. 35 No. 2 (1990)). As an application, we prove splitting of equivariant vector bundles of low rank on the wonderful compactification of an adjoint simple group in the sense of C. De Concini and C. Procesi (Lect. Notes Math. 996 (1983)). Moreover, we present an answer to a problem raised by B. Kostant in the case of complex groups.

Cited by

Related