Stabilized plethysms for the classical Lie groups

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:116

Article

Lecouver, Cedric

关键词: Characters;    Lie groups;    Symmetric functions;    Root systems;   

DOI  :  10.1016/j.jcta.2008.11.004

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free