The center of modular shifted Yangians and parabolic generators

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