Arthur Packets for $p$-adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples
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A01=Ahmed Moussaoui
A01=Andrew Fiori
A01=Bin Xu
A01=Clifton Cunningham
A01=James Mracek
Author_Ahmed Moussaoui
Author_Andrew Fiori
Author_Bin Xu
Author_Clifton Cunningham
Author_James Mracek
Category=PBF
Category=PBMW
eq_isMigrated=1
eq_nobargain
Product details
- ISBN 9781470451172
- Weight: 411g
- Dimensions: 178 x 254mm
- Publication Date: 30 Jun 2022
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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In this article we propose a geometric description of Arthur packets for padic groups using vanishing cycles of perverse sheaves. Our approach is inspired by the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups and follows the direction indicated by Vogan in his 1993 paper on the Langlands correspondence. Using vanishing cycles, we introduce and study a functor from the category of equivariant perverse sheaves on the moduli space of certain Langlands parameters to local systems on the regular part of the conormal bundle for this variety. In this article we establish the main properties of this functor and show that it plays the role of microlocalization in the work of Adams, Barbasch and Vogan. We use this to define ABV-packets for pure rational forms of p-adic groups and propose a geometric description of the transfer coefficients that appear in Arthur's main local result in the endoscopic classification of representations. This article includes conjectures modelled on Vogan's work, including the prediction that Arthur packets are ABV-packets for p-adic groups. We gather evidence for these conjectures by verifying them in numerous examples.
Clifton Cunningham, University of Calgary, Canada.
Andrew Fiori, University of Lethbridge, Canada.
Ahmed Moussaoui, Universite Versailles Saint Quentin, France.
James Mracek, University of Toronto, Canada.
Bin Xu, Tsinghua University, China.
Andrew Fiori, University of Lethbridge, Canada.
Ahmed Moussaoui, Universite Versailles Saint Quentin, France.
James Mracek, University of Toronto, Canada.
Bin Xu, Tsinghua University, China.
