On the good filtration dimension of Weyl modules for a linear algebraic group

Details On the good filtration dimension of Weyl modules for a linear algebraic group On the good filtration dimension of Weyl modules for a linear algebraic group

2005-07-27

arxiv.org/abs/math/0507552v1

J. reine angew. Math. 562 (2003), 5-21

Mathematics

Representation Theory

17 pages, uses amsart v. 2.08

Scientific paper

Let G be a linear algebraic group over an algebraically closed field of characteristic p whose corresponding root system is irreducible. In this paper we calculate the Weyl filtration dimension of the induced G-modules, \nabla(\lambda) and the simple G-modules L(\lambda), for \lambda a regular weight. We use this to calculate some Ext groups of the form Ext^*(\nabla(\lambda),\Delta(\mu)), Ext^*(L(\lambda),L(\mu)), and Ext^*(\nabla(\lambda), \nabla(\mu)), where \lambda, \mu are regular and \Delta(\mu) is the Weyl module of highest weight \mu. We then deduce the projective dimensions and injective dimensions for L(\lambda), \nabla(\lambda) and \Delta(\lambda) for \lambda a regular weight in associated generalised Schur algebras. We also deduce the global dimension of the Schur algebras for GL_n, S(n,r), when p>n and for S(mp,p) with m an integer.

Affiliated with

Also associated with

No associations

Rating

On the good filtration dimension of Weyl modules for a linear algebraic group 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 good filtration dimension of Weyl modules for a linear algebraic group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the good filtration dimension of Weyl modules for a linear algebraic group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-494909