Genericity equivariance conjecture for L-packets

Let $G$ be a quasi-split connected reductive group over a local field $k$ of characteristic zero, with maximal torus $T$ and adjoint torus $T_{\operatorname{ad}}=T/Z$. Let $\varphi$ be a Langlands parameter, let $\Pi_{\varphi}$ be its $L$-packet, and choose a parametrization $\rho\mapsto\pi_{\rho}$ by $\widehat{\mathcal{S}_{\varphi}}$. Let $\zeta_{\varphi}:T_{\operatorname{ad}}(k)/p(T(k))\to\widehat{\mathcal{S}_{\varphi}}$ be the map defined in the text. Genericity equivariance conjecture. A representation $\pi_{\rho}\in\Pi_{\varphi}$ is $\psi$-generic if and only if $\pi_{t\cdot\rho}$ is $t\cdot\psi$-generic for all $t\in T_{\operatorname{ad}}(k)$, where $t\cdot\rho:=\rho\otimes\zeta_{\varphi}(t)$. This describes the expected compatibility between the parametrization of generic $L$-packets and the action on Whittaker data; the supplied text gives no resolution status.