Micro-packets containing generic representations

Abstract

For a real group $G$, it is known from the work of Kostant and Vogan that the L-packet associated with an L-parameter $\ddot{I}†$ of $G$ contains a \emph{generic} representation if and only if the ${}^{\vee }G$-orbit in the variety of geometric parameters corresponding to $\ddot{I}†$ is open. In these notes, we generalize this result slightly by proving that the same equivalence holds when the L-packet of $\ddot{I}†$ is replaced by the micro-packet attached to $\ddot{I}†$ by Adams-Barbasch-Vogan. As a corollary, we deduce the Enhanced Shahidi Conjecture for real groups: the Arthur packet attached to an A-parameter $\ddot{I}ˆ$ of $G$ contains a generic representation if and only if $\ddot{I}ˆ{|}_{{\mathrm{SL}}_2}$ is trivial.

15 pages