8 problems

Let $\psi$ be an Arthur parameter, let $\varphi_{\psi}$ be its associated Langlands parameter, and let $\Pi(\varphi_{\psi})$ be the $L$-packet associated to $\varphi_{\psi}$. A rep…

Let $k$ be a number field and let $\pi$ be a cuspidal automorphic representation of $\operatorname{GL}_n(\mathbb{A}_k)$. A local component $\pi_v$ is tempered when its local repres…

Let $\pi=\pi(\lambda,s,{{\mathcal O}}^\vee_{\lambda,s},{{\mathcal L}}^\vee)$ be an irreducible representation in the tempered $L$-packet…

Let $G$ be a reductive group over the global function field $K$, let $[\Pi]$ be a cuspidal automorphic representation of $G([\mathbf A_K])$ with coefficients in $\bar{\mathbb Q}$,…

Asymptotic Schur orthogonality relations. There exist $\mathbf{d}(V)\in{\mathbb Z}_{\ge 0}$ and $\mathbf{f}(V)\in{\mathbb R}_{>0}$ such that, for all $v_1,v_2,v_3,v_4\in V$,

Let $\mathfrak h$ be a complex semisimple Lie algebra and $V$ an orthogonal representation of $\mathfrak h$ over $\mathbb C$. AGS equivalence conjecture. One has … This is the comp…

Let $\mathfrak h$ be a real semisimple Lie algebra and $V$ an orthogonal representation of $\mathfrak h$. AGS conjecture. If $V$ has AGS in $\mathfrak h$, then … The conjecture giv…

Point-independence conjecture. The subcategory $\Dmod^x_{\on{temp}}(\Bun_G)\subset\Dmod(\Bun_G)$ is independent of the choice of the point $x\in X$. This is deduced in the source a…