Centralizer construction of the Yangian of the queer Lie superalgebra

Consider the complex matrix Lie superalgebra $g{l}_{N\mathrm{\mid }N}$ with the standard generators $E_{ij}$ where $i,j=-N,\mathrm{.}\mathrm{.}\mathrm{.},-1,1,\mathrm{.}\mathrm{.}\mathrm{.},N$. Define an involutive automorphism $\eta$ of $g{l}_{N\mathrm{\mid }N}$ by $\eta (E_{ij})=E_{-i,-j}$. The queer Lie superalgebra $q_N$ is the fixed point subalgebra in $g{l}_{N\mathrm{\mid }N}$ relative to the automorphism $\eta$. Consider the twisted polynomial current Lie superalgebra $g=\{X(t)\in {\text{gl}}_{N\mathrm{\mid }N}[t]:\eta (X(t))=X(-t)\}$. The enveloping algebra $U(g)$ of the Lie superalgebra $g$ has a deformation, called the Yangian of $q_N$. For each $M=1,2,\mathrm{.}\mathrm{.}\mathrm{.}$ denote by $A_N^M$ the centralizer of $q_M\subset q_{N+M}$ in the superalgebra $U(q_{N+M})$. We describe the projective limit of the sequence of centralizer algebras $A_N^1,A_N^2,\mathrm{.}\mathrm{.}\mathrm{.}$ in terms of the Yangian of $q_N$.