The centre of the modular super Yangian Ym|n$Y_{m|n}$

Abstract

The present paper is devoted to studying the super Yangian 𝑌 𝑚|𝑛 associated to the general linear Lie superalgebra 𝔤𝔩 𝑚|𝑛 over a field of positive characteristic.We extend Drinfeld-type presentations of 𝑌 𝑚|𝑛 and the special super Yangian 𝑆𝑌 𝑚|𝑛 to positive characteristic.Moreover, the centre 𝑍(𝑌 𝑚|𝑛 ) of 𝑌 𝑚|𝑛 is described: it is generated by its Harish-Chandra centre together with a large 𝑝-centre. We also study the 𝑝-centre of 𝑆𝑌 𝑚|𝑛 and provide another description of the 𝑝-centre of 𝑌 𝑚|𝑛 in terms of the RTT generators.