The center of the walled Brauer algebra $B_{r,1}(δ)$
We show that the centre of the walled Brauer algebra $B_{r,1}(δ)$ over the complex field $\mathbb{C}$, for any parameter $δ\in \mathbb{C}$, is generated by the supersymmetric polynomials evaluated at the Jucys-Murphy elements. Moreover, we prove that its dimension is independent of the parameter $δ$.
math.RT↗