Characteristic maps for the Brauer algebra

Details Characteristic maps for the Brauer algebra Characteristic maps for the Brauer algebra

2011-12-03

arxiv.org/abs/1112.0620v1

Mathematics

Representation Theory

22 pages

Scientific paper

The classical characteristic map associates symmetric functions to characters of the symmetric groups. There are two natural analogues of this map involving the Brauer algebra. The first of them relies on the action of the orthogonal or symplectic group on a space of tensors, while the second is provided by the action of this group on the symmetric algebra of the corresponding Lie algebra. We consider the second characteristic map both in the orthogonal and symplectic case, and calculate the images of central idempotents of the Brauer algebra in terms of the Schur polynomials. The calculation is based on the Okounkov--Olshanski binomial formula for the classical Lie groups. We also reproduce the hook dimension formulas for representations of the classical groups by deriving them from the properties of the primitive idempotents of the symmetric group and the Brauer algebra.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-697708