2007/03/17 by Cédric Lecouvey, Lecouvey, Cedric
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.math/0703514
openalex publication_date 2007/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.