2018/03/18 by Jørgen Rasmussen, Rasmussen, Jorgen
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1803.06592
openalex publication_date 2018/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathfrakg be a finite-dimensional simple complex Lie algebra. A layer sum is introduced as the sum of formal exponentials of the distinct weights appearing in an irreducible \mathfrakg-module. It is argued that the character of every finite-dimensional irreducible \mathfrakg-module admits a decomposition in terms of layer sums, with only non-negative integer coefficients. Ensuing results include a new approach to the computation of Weyl characters and weight multiplicities, and a closed-form expression for the number of distinct weights in a finite-dimensional irreducible \mathfrakg-module. The latter is given by a polynomial in the Dynkin labels, of degree equal to the rank of \mathfrakg.