Modular orthogonal Yangians

TL;DR

This paper investigates the structure of extended orthogonal Yangians related to Lie algebras of types B and D over fields of positive characteristic, focusing on their centers and explicit descriptions.

Contribution

It introduces the $p$-center for these Yangians and provides an explicit description of the center in terms of Drinfeld generators, highlighting the role of the Harish-Chandra center and a large $p$-center.

Findings

The $p$-center for orthogonal Yangians is explicitly described.

The center is generated by the Harish-Chandra center and a large $p$-center.

The structure of the center is clarified in positive characteristic settings.

Abstract

We study the (extended) orthogonal Yangians associated to the Lie algebras types $B$ and $D$ over a field of positive characteristic. We define the $p$-center for the Yangians and obtain an explicit description of the center in terms of Drinfeld generators, showing that the center is generated by its Harish-Chandra center together with a large $p$-center.