5 problems

Let $G$ be a reductive group over a nonarchimedean local field $F$, let $\varphi$ be a discrete Langlands parameter, and let $\pi \in \Pi_{\varphi}^2(G,F)$ correspond to an irreduc…

Haines–Opdam formula conjecture. The same formula holds for the full affine Hecke algebra.

Hiraga--Ichino--Ikeda's formal degree conjecture. Suppose that $\pi\in\Pi(\mathbf{G})$ is a discrete series representation whose $L$-parameter is $\phi$. Then

Let $G_2$ be the split group of type $G_2$ over a nonarchimedean local field with residue field $\mathbb{F}_q$, let $\sigma$ be a unipotent cuspidal representation of…

Let $G$ be a connected reductive group over $F$. For a tempered $L$-parameter $\phi$, let $\Pi_\phi(G)$ be its $L$-packet, let $\widetilde{\mathcal{S}}_\phi$ be the associated S-gr…