The center of modular shifted Yangians and parabolic generators

TL;DR

This paper characterizes the center of shifted Yangians for fgl_n in positive characteristic, revealing it is generated by the Harish-Chandra center and p-center, using parabolic generators.

Contribution

It provides an explicit description of the center of shifted Yangians in positive characteristic, highlighting the roles of parabolic generators, Harish-Chandra center, and p-center.

Findings

Center is generated by Harish-Chandra and p-centers.

Explicit description of the center in terms of parabolic generators.

Advances understanding of shifted Yangians in positive characteristic.

Abstract

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.