Multiplicity formulas for fundamental strings of representations of classical Lie algebras

2017/06/30 by Emilio A. Lauret, Fiorela Rossi Bertone
Mathematics · #Adjoint representation of a Lie algebra #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Affine Lie algebra #Algebra over a field #Algebraic structures and combinatorial models #Fundamental representation #Lie algebra #Lie conformal algebra #Multiplicity (mathematics) #Representation of a Lie group #Simple Lie group #math.RT #msc:17B10 #msc:17B22 #msc:22E46

paper · pdf · doi:10.1063/1.4993851

published as J. Math. Phys. 58 (2017), 111703

openalex created_date 2017/07/14 · openalex publication_date 2017/11/01 · arxiv created 2017/11/29 · arxiv updated 2017/12/01 · openalex updated_date 2026/08/05

Abstract

We call the p-fundamental string of a complex simple Lie algebra to the sequence of irreducible representations having highest weights of the form kω1 + ωp for k ≥ 0, where ωj denotes the jth fundamental weight of the associated root system. For a classical complex Lie algebra, we establish a closed explicit formula for the weight multiplicities of any representation in any p-fundamental string.

Citations

• Vector partition function and representation theory
• Young-diagrammatic methods for the representation theory of the classical groups of type Bn, Cn, Dn
• Paths and Root Operators in Representation Theory
• Some results on generating functions for characters and weight multiplicities of the Lie algebra A₃