English

Micro-packets containing generic representations

Representation Theory 2025-10-31 v1

Abstract

For a real group GG, it is known from the work of Kostant and Vogan that the L-packet associated with an L-parameter φ\varphi of GG contains a \emph{generic} representation if and only if the G{}^{\vee}G-orbit in the variety of geometric parameters corresponding to φ\varphi is open. In these notes, we generalize this result slightly by proving that the same equivalence holds when the L-packet of φ\varphi is replaced by the micro-packet attached to φ\varphi by Adams-Barbasch-Vogan. As a corollary, we deduce the Enhanced Shahidi Conjecture for real groups: the Arthur packet attached to an A-parameter ψ\psi of GG contains a generic representation if and only if ψSL2\psi|_{\mathrm{SL}_2} is trivial.

Cite

@article{arxiv.2510.26343,
  title  = {Micro-packets containing generic representations},
  author = {Nicolas Arancibia Robert},
  journal= {arXiv preprint arXiv:2510.26343},
  year   = {2025}
}

Comments

15 pages

R2 v1 2026-07-01T07:13:34.800Z