Multiplicity formulas for fundamental strings of representations of classical Lie algebras

摘要

We call the p-fundamental string of a complex simple Lie algebra to the sequence of irreducible representations having highest weights of the form k omega(1) + omega(p) for k >= 0, where omega(j) 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. Published by AIP Publishing.