= sl3 interlacing character formula
{title2=$\chi_{a,b}=\sum_{b\leq p\leq a+b}\sum_{0\leq q\leq b}\sum_{q\leq r\leq p}x_1^r x_2^{p+q-r}x_3^{a+2b-p-q}$}
For the <special linear Lie algebra> $\mathfrak{sl}_3$, the irreducible <highest-weight representation> with <Dynkin labels> $(a,b)$ has the displayed <formal character> on diagonal matrices with $x_1x_2x_3=1$. The interlacing rows $(a+b,b,0)$, $(p,q)$ and $(r)$ enumerate a <Gelfand–Tsetlin basis>; each triple contributes the exponent differences $(r-(p+q-r),(p+q-r)-(a+2b-p-q))$ as its weight. This gives exact integer <weight multiplicities>, including repeated weights, without floating-point character evaluation.
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