108 problems

Let $F$) be a totally real field and let … be a continuous, irreducible and totally odd representation. Let $D$ be a quaternion algebra over $F$ that splits at exactly one infinite…

Let $T\subset G$ be a maximal torus split over $F$, with root datum $(X(T),\Phi(T),X^{\vee}(T),\Phi^{\vee}(T))$, and let $G^\sphat$ be the dual group. Define … and let…

Let $K$ be a finite extension of $\mathbb{Q}_p$. Write $\mathcal{D}(\ast/GL_n(K)^{\la})$ for the stable $\infty$-category of locally analytic representations of $GL_n(K)$, let…

Let $F$ be a non-archimedean local field, let $G$ be a connected reductive $F$-group, and let $\Pi_{\varphi}(G)$ be a discrete series $L$-packet of irreducible smooth representatio…

Let $G$ be a connected reductive group, let $G_\eta$ range over its pure inner forms, and let $\mathbb{L}^u_{\underline q}$ be the graded unipotent Langlands parameter space. Write…

Let $G$ be a reductive group over a non-Archimedean field, let $\phi$ be an $L$-parameter, and let $\Pi_{\phi}^{\mathrm{ABV}}$ denote its ABV-packet. Let $\widehat{\phi}$ be the Py…

Let $G$ be a reductive group and let $\pi$ be an irreducible admissible representation of $G$. Define $\Psi(\pi)=\\{\psi\in\Psi^+(G)\mid \pi\in\Pi_\psi\\}$, let $\phi_\psi$ be the…

Let $H$ be a $p$-adic symplectic group or split special orthogonal group, and in the special even orthogonal case let $H^+$ be the corresponding full even orthogonal group. Let…

Let $F$ be a $p$-adic field, let $W_F'$ be its Weil–Deligne group, and let $G$ be a connected reductive $p$-adic group. Let $\Pi(G/F)$ be the set of isomorphism classes of irreduci…

Let $u$ be a closed point of $U$, let $\LS_{\prescript{L}{}{G},F_u}$ be the local Langlands parameter stack, and let $\LS_{\prescript{L}{}{G},\cO_u}$ denote its unramified locus. L…

Let $F$ be a local field, let $G$ be a quasisplit reductive group over $F$, and let $B$ be a Borel subgroup with unipotent radical $N$. Choose a generic continuous character…

Let $\varphi\colon W_F\to{{}^LG}({\overline{\mathbb{Q}}_\ell})$ be a semisimple $L$-parameter of Langlands–Shahidi type, and let ${\mathcal{F}}_\varphi$ be the corresponding Hecke…

Let $G$ be a reductive group and let $V\in{\operatorname{Rep}}(G)$, with $V^\vee$ its dual representation. Let ${\mathcal{P}}_V^{\operatorname{norm}}$ denote the normalized period…

Let $G$) be a connected quasi-split reductive group over $F$ with a fixed Whittaker datum. Suppose there is a categorical equivalence … For a dual pair…

Let $Z^1(W_F,\widehat{G})$ be the moduli of L-parameters over $\overline{\mathbb{Q}}_{\ell}$ for $\mathbf{G}$, let $C_{[\varphi]}$ be the connected components containing a lift of…

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 $F$ be the underlying non-Archimedean local field, let $n$ be a positive integer, and let $\pi_{1}$ and $\pi_{2}$ be irreducible supercuspidal representations of…

Let $\check G$ be a connected reductive algebraic group over $F=\mathbb{Q}_p$, let $G$ be its Langlands dual group, and let $\Lambda:W_F\to{}^L\check G$ be an infinitesimal charact…

Let $n$, $r$, $k_i$, and $m_i$ be as above, and let $\psi^\BR$ denote the corresponding parameter on the complex side. On the $p$-adic side, let $\psi^p$ and the Arthur–Vogan packe…

Let $(G,X)$ and $(G',X')$ be Shimura data with $G'$ a prime-to-$p$ trivialized inner form of $G$, and let $K'_p\subset G'({\mathbb Q}_p)$ be open compact. Let $\Loc_{\widehat G,p}$…

Assume that $G$ is quasi-split over $F$, equipped with a pinning $(B,T,e)$, and fix a non-trivial additive character $\psi:F\to {\mathbb Z}_\ell[\mu_{p^\infty}]^\times$. Let…

Assume the $p$-adic Kazhdan–Lusztig hypothesis. Let $\phi$ be a Langlands parameter, let $\lambda_\phi$ be its infinitesimal parameter, and let $C_\phi$ be the orbit associated to…

Let $G$ be a reductive $p$-adic group and let $\phi$ be a Langlands parameter, with associated L-packet $\Pi_\phi(G)$. A representation is generic if it admits a Whittaker model. G…

Braverman–Kazhdan local $\rho$-Fourier transform conjecture. There exist a $\rho$-Schwartz space, a distinguished $\rho$-basic function, and an invariant distribution satisfying al…

Let $P$ be a parabolic subgroup of $G$ with Levi subgroup $M$ and unipotent radical $U$, let $V\in\operatorname{Rep}({}^LG)$, and restrict $V$ to ${}^LP$. Choose a finite filtratio…