Micro-packets containing generic representations
Nicolas Arancibia Robert

TL;DR
This paper generalizes a known criterion for the existence of generic representations in L-packets to micro-packets, and proves the Enhanced Shahidi Conjecture for real groups, linking genericity to triviality of certain parameters.
Contribution
It extends the criterion for generic representations from L-packets to micro-packets and proves the Enhanced Shahidi Conjecture for real groups.
Findings
The equivalence between genericity and open orbits holds for micro-packets.
The Enhanced Shahidi Conjecture is proved for real groups.
Generic representations exist in Arthur packets if and only if the A-parameter is trivial on SL_2.
Abstract
For a real group , it is known from the work of Kostant and Vogan that the L-packet associated with an L-parameter of contains a \emph{generic} representation if and only if the -orbit in the variety of geometric parameters corresponding to is open. In these notes, we generalize this result slightly by proving that the same equivalence holds when the L-packet of is replaced by the micro-packet attached to by Adams-Barbasch-Vogan. As a corollary, we deduce the Enhanced Shahidi Conjecture for real groups: the Arthur packet attached to an A-parameter of contains a generic representation if and only if is trivial.
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