Parabolic presentations of Yangian in types $B$ and $C$

We establish a parabolic presentation of the extended Yangian $\text{X}({\mathfrak{g}}_N)$ associated with the Lie algebras ${\mathfrak{g}}_N$ of type $B$ and $C$, parameterized by a symmetric composition $\nu$ of $N$. By formulating a block matrix version of the RTT presentation of $\text{X}({\mathfrak{g}}_N)$, we systematically derive the generators and relations through the Gauss decomposition of the generator matrix in $\nu$-block form. Furthermore, leveraging this parabolic presentation, we obtain a novel formula for the center of $\text{X}({\mathfrak{g}}_N)$, offering new insights into its structure.