4 problems

Lapid–Mao's local conjecture. For every $\eta\in E_v^\times$ such that $\bar\eta=-\eta$, one has

Let $F=k((t))$ be a local field, let $G(F)$ be the group of $F$-rational points, and let $\pi$ be a tempered irreducible admissible representation of $G(F)$. Let $AZ(\pi)$ be its i…

Let $\psi_v$ be a local $A$-parameter, let $\Pi_{\psi_v}$ be its local $A$-packet, and let $\Pi_{\phi_{\psi_v}}\subset\Pi_{\psi_v}$ be the corresponding $L$-packet. Let $r(\pi)$ de…

Let $M$ be the Levi component of a parabolic subgroup $P$, let $M_\mathrm{ab}$ be its abelianization, and let $\mathcal{S}(X_P)$ be the Schwartz space. Choose a Haar measure…