Stabilized plethysms for the classical Lie groups

Details Stabilized plethysms for the classical Lie groups Stabilized plethysms for the classical Lie groups

2007-03-17

arxiv.org/abs/math/0703514v2

Mathematics

Representation Theory

Scientific paper

The plethysms of the Weyl characters associated to a classical Lie group by the symmetric functions stabilize in large rank. In the case of a power sum plethysm, we prove that the coefficients of the decomposition of this stabilized form on the basis of Weyl characters are branching coefficients which can be determined by a simple algorithm. This generalizes in particular some classical results by Littlewood on the power sum plethysms of Schur functions. We also establish explicit formulas for the outer multiplicities appearing in the decomposition of the tensor square of any irreducible finite dimensional module into its symmetric and antisymmetric parts. These multiplicities can notably be expressed in terms of the Littlewood-Richardson coefficients.

Affiliated with

Also associated with

No associations

Rating

Stabilized plethysms for the classical Lie groups 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 Stabilized plethysms for the classical Lie groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stabilized plethysms for the classical Lie groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-432988