Multiplicity formulas for fundamental strings of representations of classical Lie algebras

LAURET, EMILIO A.; BERTONE, FIORELA ROSSI

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 2017 vol. 58

0022-2488

We call the emph{$p$-fundamental string} of a complex simple Lie algebra to the sequence of irreducible representations having highest weights of the form $komega_1+omega_p$ for $kgeq0$, where $omega_j$ denotes the $j$-th 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.