The support of Kostant's weight multiplicity formula is an order ideal in the weak Bruhat order

Portia X. Anderson, Esther Banaian, Melanie J. Ferreri +7

For integral weights $\hat{I}»$ and $\hat{I}¼$ of a classical simple Lie algebra $\mathfrak{g}$, Kostant's weight multiplicity formula gives the multiplicity of the weight $\hat{I}¼$ in the irreduci…