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Abstract Let G be a group and let H be a subgroup of G . The classical branching rule (or symmetry breaking) asks: For an irreducible representation π of G ,determine the occurrence of an irreducible representation σ of H in the restriction of π to H . The reciprocal branching problem of this classical branching problemis to ask: For an irreducible representation σ of H , find an irreducible representation π of G such that σ occurs in the restrictionof π to H . For automorphic representations of classical groups, the branching problem has been addressed by the well-known global Gan–Gross–Prasad conjecture.In this paper, we investigate the reciprocal branching problem for automorphic representationsof special orthogonal groups using the twisted automorphic descent method as developed in [13]. The method may be applied toother classical groups as well.more » « less
