A note on the center of the queer super Yangian $\mathrm{Y}({\mathfrak{q}}_1)$

We investigate two families of central elements of the queer super Yangian $\mathrm{Y}({\mathfrak{q}}_1)$, arising from the constructions of Poletaeva-Serganova and from Nazarov’s quantum Berezinian. We establish an explicit relation between their generating series, thereby giving an answer to the question raised by Nazarov in \cite{Na22}.