Commutative subalgebra of a shuffle algebra associated with quantum toroidal ${\mathfrak{gl}}_{m|n}$

B. Feigin, M. Jimbo, E. Mukhin

We define and study the shuffle algebra $S{h}_{m|n}$ of the quantum toroidal algebra ${\mathcal{E}}_{m|n}$ associated to Lie superalgebra ${\mathfrak{gl}}_{m|n}$. We show that $S{h}_{m|n}$…