On the Fourier–Jacobi model for some endoscopic Arthur packet of $U(3) \times U(3)$: the nongeneric case

Jaeho Haan

Vol. 286 (2017), No. 1, 69–89

DOI: 10.2140/pjm.2017.286.69

Abstract

For a generic $L$-parameter of $U\left(n\right)\times U\left(n\right)$, it is conjectured that there is a unique representation in their associated relevant Vogan $L$-packet which produces the unique Fourier–Jacobi model. We investigated this conjecture for some nongeneric $L$-parameters of $U\left(3\right)\times U\left(3\right)$ and discovered that it is true for some nongeneric $L$-parameters and false for some nongeneric $L$-parameters. In the case when it holds, we specified such representation under the local Langlands correspondence for unitary groups.

Keywords

Gan–Gross–Prasad conjecture, Fourier–Jacobi model, nongeneric parameter, local theta correspondence

Mathematical Subject Classification 2010

Primary: 11F27, 11F70, 11F85

Milestones

Received: 25 November 2015

Revised: 8 June 2016

Accepted: 21 June 2016

Published: 9 December 2016