Quantum current algebra ${\bf U}(\frak{gl}_n[t])$: canonical bases and polynomial representations

We introduce a quantum deformation $\mathbf{U}(\mathfrak{gl}_n[t])$ of the universal enveloping algebra of the current algebra $\mathfrak{gl}_n[t]$, realized as a Hopf parabolic subalgebra of quantum affine $\mathfrak{gl}_n$. Unlike the Yangian---the standard quantization of the current algebra---ou