Jacquet–Rallis Fundamental Lemma for unitary Lie algebras

Let $\mathfrak{s}(E_0)$ be the symmetric Lie algebra and let $\mathfrak{u}(J_0)$ and $\mathfrak{u}(J_1)$ be the Lie algebras of the corresponding unitary groups. Let $Ω(y)$ and $O_y$ denote the transfer factor and orbital integral, and let $\mathfrak{u}(J_0)(\mathcal{O}_{E_0})$ be the integral lattice specified in the source. Jacquet–Rallis Fundamental Lemma. The function $1_{\mathfrak{s}(\mathcal{O}_{E_0})}$ and the pair $(1_{\mathfrak{u}(J_0)(\mathcal{O}_{E_0})},0)$ are transfers of each other; equivalently, for all $y\in\mathfrak{s}(E_0)_{\mathrm{rs}}$,

$$Ω(y)O_y(1_{\mathfrak{s}(\mathcal{O}_{E_0})})=\begin{cases}O_x(1_{\mathfrak{u}(J_0)(\mathcal{O}_{E_0})})&\text{if }y\text{ matches }x\in\mathfrak{u}(J_0),\\0&\text{if }y\text{ matches }x\in\mathfrak{u}(J_1). \end{cases}$$

This is the Lie algebra analogue of the group Fundamental Lemma. The source does not state a resolution status for this version.