This article is available for purchase or by subscription. See below.
Abstract
|
In 1993 David Vogan proposed a basis for the vector space of stable distributions on
-adic
groups using the microlocal geometry of moduli spaces of Langlands parameters.
In the case of general linear groups, distribution characters of irreducible
admissible representations, taken up to equivalence, form a basis for the
vector space of stable distributions. In this paper we show that these two
bases, one putative, cannot be equal. Specifically, we use the Kashiwara–Saito
singularity to find a non-Arthur type irreducible admissible representation of
-adic
whose
ABV-packet, as defined by Cunningham et al. (2022b), contains exactly one other
representation. Consequently, for general linear groups, while all A-packets are
singletons, some ABV-packets are not. In the course of the proof of this result, we
strengthen the main result concerning the Kashiwara–Saito singularity by Kashiwara
and Saito (1997).
|
PDF Access Denied
We have not been able to recognize your IP address
18.188.152.162
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
admissible representations, Arthur parameters, L-packets,
Langlands correspondence, Kashiwara–Saito singularity,
perverse sheaves, vanishing cycles
|
Mathematical Subject Classification
Primary: 11F70, 22E50, 32S30
Secondary: 32S60
|
Milestones
Received: 16 December 2021
Revised: 13 August 2022
Accepted: 25 October 2022
Published: 21 March 2023
|
© 2022 MSP (Mathematical Sciences
Publishers). |
|