Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2002; 39(3): 331-349

Printed May 1, 2002

Copyright © The Korean Mathematical Society.

Stable class of equivariant algebraic vector bundles over representations

Mikiya Masuda

Osaka City University

Abstract

Let $G$ be a reductive algebraic group and let $B, F$ be $G$-modules. We denote by $\text{VEC}_G(B,F)$ the set of isomorphism classes in algebraic $G$-vector bundles over $B$ with $F$ as the fiber over the origin of $B$. Schwarz (or Kraft-Schwarz) shows that $\text{VEC}_G(B,F)$ admits an abelian group structure when $\dim B/\!\!/G=1$. In this paper, we introduce a stable functor $\text{VEC}_G(B,F^\infty)$ 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

MSC numbers: Primary 14D20; Secondary 14R20

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