13 problems

Let $F/F_0$ be the unramified quadratic extension and let $G(\mathbb{W})\times G(\mathbb{V})$ act on the formal scheme $\mathcal{N}_{m,n}$. For a regular element…

Let $\varphi'\in\mathcal{H}_{K'^{{{{{{{{\flat}}}}}}}}}\otimes\mathcal{H}_{K'}$, and let…

Let $S_{n+1}$ be the relevant symmetric space, let $\mathcal{H}_K$ be its spherical Hecke algebra, and let…

Let $G'_{\mathrm{rs},W_1}$ be the open subset of $\operatorname{GL}_n(F)\times\operatorname{GL}_{n+1}(F)$ consisting of regular semisimple elements matching with elements in the no…

Assume that $F/F_0$ is an unramified quadratic extension of $p$-adic fields for an odd prime $p$, and retain the groups $G(V_0)$ and $G(V_1)$, the symmetric space $S_n(F_0)$, and t…

Let $(x,j)$ be a pair in the odd hermitian setting. It is regular semi-simple and self-adjoint as defined in the source, and it is artinian when the schematic intersection…

Let $\mathfrak{s}(E_0)$ be the symmetric Lie algebra and let $\mathfrak{u}(J_1)$ be the Lie algebra of the odd unitary group. Let $Ω(y)$ and $\partial O_y$ denote the transfer fact…

Let $S(E_0)$ be the relevant symmetric space, let $U(J_1)$ be the unitary group attached to the odd hermitian form, and let $Ω(γ)$, $\partial O_γ(1_{S(\mathcal{O}_{E_0})})$, and…

Let $S(E_0)$ be the relevant symmetric space, let $U(J_1)$ be the unitary group attached to the odd hermitian form, and let $Ω(γ)$, $\partial O_γ(1_{S(\mathcal{O}_{E_0})})$, and…

Assume $F/F_0$ is unramified and use the notation for $G'$, $S$, $\mathfrak{s}$, their matching unitary groups, transfer factors, and intersection numbers established in the source…

Assume that $F/F_0$ is unramified. Let $K'\subset S_n(F_0)$ and $K_1\subset\mathrm{U}(W_1)(F_0)$ be as in the almost self-dual transfer conjecture, let $\omega_S$ be the transfer f…

Assume that $F/F_0$ is unramified, the special vectors $u_i$ have norm one, and use the same Haar measure and transfer factor as in the unramified fundamental lemma. Let…

Assume that $F/F_0$ is unramified. Let $\gamma\in S_n(F_0)_{\mathrm{rs}}$ match $g\in\mathrm{U}(W_1)(F_0)_{\mathrm{rs}}$, let $q$ be the residue-field cardinality, and write…