On fusion product and N!/k-conjecture

We formulate a version of Schur--Weyl duality for the current Lie algebra $\mathfrak{gl}_V[x,y]=\mathfrak{gl}_V\otimes\mathbb{C}[x,y]$. Under this duality, the Garsia--Haiman modules of the $N!$-conjecture become cyclic and cocyclic $\mathfrak{gl}_V[x,y]$-modules, and we describe them as iterated fu