The coideal conjecture for the twisted affine Yangian of type D

Let $TY_\hbar(\widehat{\mathfrak{so}}(2n))$ be the associative algebra generated by

$$\{H_{i,0},H_{j,1},X^\pm_{i,r}\mid 0\leq i\leq n,1\leq j\leq n-1,r=0,1\}$$

with the defining relations specified in the paper. Let the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ be the corresponding affine Yangian algebra. The coideal conjecture. The associative algebra $TY_\hbar(\widehat{\mathfrak{so}}(2n))$ becomes a coideal of the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ and can be regarded as the twisted affine Yangian of type $D$. This conjecture proposes a coideal realization of the newly defined twisted affine Yangian, motivated by the decomposition of the Dynkin diagram of $\widehat{\mathfrak{so}}(2n)$ into two Dynkin diagrams of $\mathfrak{so}(2n)$; the claimed coideal structure and identification remain to be established.