Multiplicity formulas for fundamental strings of representations of classical Lie algebras

LAURET, EMILIO AGUSTÍN; ROSSI BERTONE, FIORELA

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 2017 vol. 58

0022-2488

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.