On restriction of unitarizable representations of general linear groups and the non-generic local Gan–Gross–Prasad conjecture

We prove one direction of a recently posed conjecture by Gan-Gross-Prasad, which predicts the branching laws that govern restriction from p-adic $GL_n$ to $GL_{n-1}$ irreducible smooth representations within Arthur-type class. We extend this prediction full class unitarizable representations, exhibiting combinatorial relation must be satisfied for any pair in appears as quotient other. settle cases either is generic. The method proof involves transfer problem, using Bernstein decomposition and quantum affine Schur-Weyl duality, into realm algebras. This restatement problem allows an application combined power result Hernandez on cyclic modules together with Lapid-Minguez criterion setting.