On the Weak Local Arthur Packets Conjecture for Split Classical Groups

Author:

Liu Baiying1,Lo Chi-Heng1

Affiliation:

1. Department of Mathematics Purdue University West Lafayette , IN 47907, USA

Abstract

Abstract Recently, motivated by the theory of real local Arthur packets, making use of the wavefront sets of representations over non-Archimedean local fields $F$, Ciubotaru, Mason-Brown, and Okada defined the weak local Arthur packets consisting of certain unipotent representations and conjectured that they are unions of local Arthur packets. In this paper, we prove this conjecture for $\textrm{Sp}_{2n}(F)$ and split $\textrm{SO}_{2n+1}(F)$ with the assumption of the residue field characteristic of $F$ being large. In particular, this implies the unitarity of these unipotent representations. We also discuss the generalization of the weak local Arthur packets beyond unipotent representations, which reveals the close connection with a conjecture of Jiang on the structure of wavefront sets for representations in local Arthur packets.

Publisher

Oxford University Press (OUP)

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