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

TL;DR

This paper proves a local Gan-Gross-Prasad conjecture for non-tempered representations of general linear groups over non-Archimedean fields, extending to Bessel, Fourier-Jacobi models, and exploring Ext-branching laws.

Contribution

It establishes the conjecture for non-tempered cases and generalizes the results to Bessel and Fourier-Jacobi models, also investigating potential Ext-branching law extensions.

Findings

Proved the local Gan-Gross-Prasad conjecture for non-tempered representations.

Extended the theory to Bessel and Fourier-Jacobi models.

Explored possible generalizations to Ext-branching laws.

Abstract

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