  New graded modules for the current algebra of $\mathfrak{sl}_n$ are
introduced. Relating these modules to the fusion product of simple
$\mathfrak{sl}_n$-modules and local Weyl modules of truncated current algebras
shows their expected impact on several outstanding conjectures. We further
generalize results on PBW filtrations of simple $\mathfrak{sl}_n$-modules and
use them to provide decomposition formulas for these new modules in important
cases.
