 3

For $f,g\in \mathcal{E}$, define their convolution byThe 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 ${\delta }_{\mu }\ast {\delta }_{\nu }={\delta }_{\mu +\nu }$.