A survey on the restriction problem of $p$-adic unitary group for some non-generic $L$-parameter (Representation theory and various problems in algebra, analysis, and geometry)

Abstract

The local Gan-Gross-Prasad conjecture of unitary groups, which is now settled by the works of Beuzart-Plessis, Gan and Ichino, says that for a pair of generic L-parameters of (U(n+1), U(n)), there is a unique pair of representations in their associated Vogan L-packets which produces the Bessel model. In this survey article, we report that the conjecture does not hold for a non-generic case.