Shifted twisted Yangians and affine Grassmannian islices

In a prequel we introduced the shifted iYangians ${}^\imath Y_μ$ associated to quasi-split Satake diagrams of type ADE and even spherical coweights $μ$, and constructed the iGKLO representations of ${}^\imath Y_μ$, which factor through truncated shifted iYangians ${}^\imath Y_μ^λ$. In this paper, we show that ${}^\imath Y_μ$ quantizes the involutive fixed point locus ${}^\imath W_μ$ arising from affine Grassmannians of type ADE, and supply strong evidence toward the expectation that ${}^\imath Y_μ^λ$ quantizes a top-dimensional component of the affine Grassmannian islice ${}^\imath\overline{W}_μ^λ$. We identify the islices ${}^\imath\overline{W}_μ^λ$ in type AI with suitable nilpotent Slodowy slices of type BCD, building on the work of Lusztig and Mirković-Vybornov in type A. We propose a framework for producing ortho-symplectic (and hybrid) Coulomb branches from split (and nonsplit) Satake framed double quivers, which are conjectured to relate closely to the islices ${}^\imath\overline{W}_μ^λ$ and the algebras ${}^\imath Y_μ^λ$.