The center of modular shifted Yangians and parabolic generators

This paper is devoted to the study of the shifted Yangian $Y_n\left(\sigma \right)$ associated to the general linear Lie algebra ${\mathrm{gl}}_n$ over a field of positive characteristic. We obtain an explicit description of the center $Z\left(Y_n\right(\sigma \left)\right)$ of $Y_n\left(\sigma \right)$ in terms of parabolic generators, showing that it is generated by its Harish-Chandra center and its p-center.