= Shell multiplicities in an SU(3) weight diagram
{title2=$m_{p,q}(\mu)=\sum_{k=0}^{\min(p,q)}\mathbf1_{P_{p-k,q-k}}(\mu)$}
Let $P_{a,b}$ be the convex hull of the <Weyl group> orbit of the <highest weight> $a\omega_1+b\omega_2$ for the <SU(3) Lie algebra>. Restrict the displayed formula to the <weight lattice> coset $p\omega_1+q\omega_2+$ root lattice. It describes successive inward shells: the outer boundary has <weight multiplicity> one, each inward shell increases it by one, and the final triangular region has the constant value $\min(p,q)+1$. When $p=q$ that region is a single point. A triangular diagram with $p=0$ or $q=0$ has multiplicity one throughout. This is a geometric form of the <dominant weight multiplicity formula for sl3>, transported by Weyl reflections.
// Target: lie-theory.bigb
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