The Brauer algebra and the symplectic Schur algebra

Details The Brauer algebra and the symplectic Schur algebra The Brauer algebra and the symplectic Schur algebra

2008-06-27

arxiv.org/abs/0806.4500v3

Mathematics

Representation Theory

Scientific paper

Let k be an algebraically closed field of characteristic p>0, let m,r be integers with m\ge1, r\ge0 and m\ge r and let S_0(2m,r) be the symplectic Schur algebra over k as introduced by the first author. We introduce the symplectic Schur functor, derive some basic properties of it and relate this to work of Hartmann and Paget. We do the same for the orthogonal Schur algebra. We give a modified Jantzen sum formula and a block result for the symplectic Schur algebra under the assumption that r and the residue of 2m mod p are small relative to p. From this we deduce a block result for the orthogonal Schur algebra under similar assumptions. Finally, we deduce from the previous results a new proof of the geometric description of the blocks of the Brauer algebra in characteristic 0 as obtained by Cox, De Visscher and Martin.

Affiliated with

Also associated with

No associations

Rating

The Brauer algebra and the symplectic Schur algebra 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 The Brauer algebra and the symplectic Schur algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Brauer algebra and the symplectic Schur algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-692863