arXiv subjects

Nicolas Arancibia Robert

Publications and source records attributed to Nicolas Arancibia Robert.

5 recordsLinked to original sources

arXiv2025

Micro-packets containing generic representations

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

math.RT↗

arXiv2025

Micro-packets for real groups of type $G_2$

In their study of Arthur's conjectures for real groups, Adams, Barbasch, and Vogan introduced the notion of micro-packets. Micro-packets are finite sets of irreducible representations defined using microlocal geometric methods and characteristic cycles. We explore an action of the Weyl group on characteristic cycles to compute all micro-packets of real groups of type $G_2$.

math.RT↗

arXiv2024

Arthur packets for pure real forms of symplectic and special orthogonal groups

Arthur packets have been defined for pure real forms of symplectic and special orthogonal groups following two different approaches. The first approach, due to Arthur, Moeglin and Renard uses harmonic analysis. The second approach, due to Adams, Barbasch and Vogan uses microlocal geometry. We prove that the two approaches produce essentially equivalent Arthur packets. This extends previous work of the authors and J. Adams for the quasisplit real forms.

math.RT↗

arXiv2022

Equivalent definitions of Arthur packets for real unitary groups

Mok and Moeglin-Renard have defined Arthur packets for unitary groups. Their definitions follow Arthur's work on classical groups and rely on harmonic analysis. For real groups there is an alternative definition of Arthur packets due to Adams-Barbasch-Vogan. It relies on sheaf-theoretic techniques instead of harmonic analysis. We prove that these two definitions of Arthur packets are equivalent in the case of real unitary groups.

math.RT↗

arXiv2022

L-packets over strong real forms

Langlands defined L-packets for real reductive groups. In order to refine the local Langlands correspondence, Adams-Barbasch-Vogan combined L-packets over all real forms belonging to an inner class. Using different methods, Kaletha also defines such combined L-packets with a refinement to the local Langlands correspondence. We prove that the L-packets of Adams-Barbasch-Vogan and Kaletha are the same and are parameterized identically.

math.RT↗