3 (source code)
= 3
{scope}
For $f,g\in\mathcal E$, define their <convolution> by
$$
(f*g)(\lambda)=\sum_{\mu+\nu=\lambda}f(\mu)g(\nu).
$$
The support restrictions make each sum finite: for fixed upper-cone representatives, the <simple root> coefficients in the two downward displacements are bounded nonnegative integers. This also proves closure in $\mathcal E$ and associativity by finite reordering at each coefficient. The unit is $\delta_0$, and $\delta_\mu*\delta_\nu=\delta_{\mu+\nu}$.
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