[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2002.39.3.331

STABLE CLASS OF EQUIVARIANT ALGEBRAIC VECTOR BUNDLES OVER REPRESENTATIONS

Masuda, Mikiya (Department of Mathematics Osaka City University)

Publication Information

Journal of the Korean Mathematical Society / v.39, no.3, 2002 , pp. 331-349 More about this Journal

Abstract

Let G be a reductive algebraic group and let B, F be G-modules. We denote by $VEC_{G}$ (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that $VEC_{G}$ (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor $VEC_{G}$ (B, $F^{\chi}$ ) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.

Keywords

vector bundle; reductive algebraic group; moduli; invariant theory;

Citations & Related Records

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