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This paper generalizes the GGP conjectures which were earlier formulated fortempered or more generally generic L-packets to Arthur packets, especially forthe nongeneric L-packets arising from Arthur parameters. The paper introducesthe key notion of a relevant pair of A-parameters which governs the branchinglaws for $GL_n$ and all classical groups over both local fields and globalfields. It plays a role for all the branching problems studied in our earlierwork including Bessel models and Fourier-Jacobi models.

Branching laws for Classical Groups: the non-tempered case