On the adjoint quotient of Chevalley groups over arbitrary base schemes

Details On the adjoint quotient of Chevalley groups over arbitrary base schemes On the adjoint quotient of Chevalley groups over arbitrary base schemes

2008-05-14

arxiv.org/abs/0805.2140v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W, we show that the Chevalley morphism t/W -> g/G is an isomorphism except for the group Sp_{2n} over a base with 2-torsion. In this case this morphism is only dominant and we compute it explicitly. We compute the adjoint quotient in some other classical cases, yielding examples where the formation of the quotient g -> g/G commutes, or does not commute, with base change on S.

Affiliated with

Also associated with

No associations

Rating

On the adjoint quotient of Chevalley groups over arbitrary base schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the adjoint quotient of Chevalley groups over arbitrary base schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the adjoint quotient of Chevalley groups over arbitrary base schemes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-56322