Cho's local representation density formula for hermitian special cycles

Let $E/F$ be the unramified quadratic extension, let ${\mathbb V}$ be the space of special homomorphisms with hermitian form $h$, and let $\lbrace x_1,\dots,x_{2n}\rbrace$ be a basis of ${\mathbb V}$. Write ${\mathcal Z}(x_i)$ for the associated special cycles on ${\mathcal N}^n_{E/F}(1,2n-1)$, and set

$$B=(h(x_i,x_j))\in X_{2n}(O_E).$$

Here $\Lambda_{2n}^+$, $D_\lambda$, $A_\lambda(B)$, and ${\mathfrak b}_i^0$ are the indexing set and local-density quantities used in the formula. Cho's local representation density formula. The arithmetic intersection number satisfies

$$\langle {\mathcal Z}(x_1),\dots,{\mathcal Z}(x_{2n})\rangle=\sum_{\lambda\in\Lambda_{2n}^+}D_\lambda A_\lambda(B)-\sum_{0\leq i\leq n-1}{\mathfrak b}_i^0 A_{(1^i,0^{2n-i})}(B).$$

This conjecture relates arithmetic intersections of special cycles on unitary Rapoport–Zink spaces to derivatives and representation densities. The cited sources are presented as conjectural formulations, while the constants require the precise definitions given there.