Chern classes for representations of reductive groups

Details Chern classes for representations of reductive groups Chern classes for representations of reductive groups

2001-04-03

arxiv.org/abs/math/0104031v1

Mathematics

Algebraic Geometry

7 pages, Plain TeX

Scientific paper

Let G be a complex connected reductive group. The representation ring R(G) admits a canonical filtration defined in terms of the lambda-structure. We compute the associated graded ring gr R(G) (over Q) and the Chern classes of a representation -- an easy exercise which we have been unable to find in the literature. As an application we give a simple definition of the characteristic classes of a principal bundle P --> B in gr K(B), and a simple way of computing the Chern classes of the associated vector bundles.

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