6 problems

Let $0\leq r\leq n+1$, let $\varepsilon$ be the parity of $r$, and let $W_\varepsilon$ and $W_{\varepsilon+1}$ be the hermitian spaces of dimension $n+1$ with opposite invariants.…

Arithmetic transfer conjecture for odd type $(r,0)$. There exists $\varphi'\in C_c^\infty(G')$ transferring to $(c_r^2\\,\mathbf{1}_{K_n^{[r]}\times K_{n+1}},0)$ such that, for eve…

Assume that $F/F_0$ is ramified and that $n\geq2$ is even. Let $K_0^{{{{{{{{\flat}}}}}}}}$ be the stabilizer of an almost $\pi$-modular lattice and let $K_0^+$ and $K_0^-$ be the s…

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…

Lie algebra arithmetic transfer conjecture. (a) There exists $\phi'\in C_c^\infty(\mathfrak{s})$ transferring to $(\mathbf{1}_{\mathfrak{k}_0},0)$ such that, whenever matching…

Let $F/F_0$ be ramified and let $n\geq3$ be odd. Let $S(F_0)$ be the inhomogeneous symmetric space, let $U_0$ and $U_1$ be the relevant unitary groups, let $K_0\subset U_0(F_0)$ be…