A note on the center of the super Yangian $Y_{M|N}(\mathfrak{s})$

TL;DR

This paper introduces a new formula for the quantum Berezinian of the super Yangian $Y_{M|N}(rak{s})$, expanding the understanding of its algebraic structure through parabolic generators.

Contribution

It provides a generalized expression for the quantum Berezinian using parabolic generators, extending previous formulas based on RTT and Drinfeld generators.

Findings

New formula for the quantum Berezinian using parabolic generators

Generalization of previous expressions in terms of RTT and Drinfeld generators

Enhanced understanding of the super Yangian's algebraic structure

Abstract

Let $Y_{M|N}(\mathfrak{s})$ be the super Yangian associated with an arbitrary fixed $0^M1^N$-sequence $\mathfrak{s}$. In the present paper, we give a new formula for the quantum Berezinian by using the parabolic generators, which generalizes the usual expression in terms of RTT generators or Drinfeld generators.