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Equivariant algebraic vector bundles over representations of reductive groups: theory.

Abstract：

:Let G be a reductive algebraic group and let B be an affine variety with an algebraic action of G. Everything is defined over the field C of complex numbers. Consider the trivial G-vector bundle B x S = S over B where S is a G-module. From the endomorphism ring R of the G-vector bundle S a construction of G-vector bundles over B is given. The bundles constructed this way have the property that when added to S they are isomorphic to F + S for a fixed G-module F. For such a bundle E an invariant rho(E) is defined that lies in a quotient of R. This invariant allows us to distinguish nonisomorphic G-vector bundles. This is applied to the case where B is a G-module and, in that case, an invariant of the underlying equivariant variety is given too. These constructions and invariants are used to produce families of inequivalent G-vector bundles over G-modules and families of inequivalent G actions on affine spaces for some finite and some connected semisimple groups.

journal_name

Proc Natl Acad Sci U S A

journal_title

Proceedings of the National Academy of Sciences of the United States of America

authors

Masuda M,Petrie T

doi

10.1073/pnas.88.20.9061

keywords:

subject

Has Abstract

pub_date

1991-10-15 00:00:00

pages

9061-4

issue

20

eissn

0027-8424

issn

1091-6490

journal_volume

88

pub_type

杂志文章

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