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We prove a local Gan-Gross-Prasad conjecture on predicting the branching lawfor the non-tempered representations of general linear groups in the case ofnon-Archimedean field. We also generalize to Bessel and Fourier-Jacobi modelsand study a possible generalization to Ext-branching laws.

Restriction for general linear groups: the local non-tempered Gan-Gross-Prasad conjecture (non-Archimedean case)