Chen, Cheng2024-08-222024-08-222024-06https://hdl.handle.net/11299/265114University of Minnesota Ph.D. dissertation. June 2024. Major: Mathematics. Advisor: Dihua Jiang. 1 computer file (PDF); iii, 85 pages.The local Gan-Gross-Prasad conjecture is a generalization of the branching problem toclassical groups over local fields of characteristic zero. The conjecture speculates on the multiplicity, that is, the dimension of the Bessel models and Fourier-Jacobi models in an irreducible admissible representation. Equivalent conditions for the multiplicity equaling to one is given in [GP92, GP94, GGP12]. J.-L. Waldspurger did the pioneer’s work and proved the Bessel special orthogonal cases for tempered parameters over non-Archimedean local fields in [Wald10, Wald12a, Wald12b, Wald12c]. C. Mœglin and Waldspurger proved that case for generic parameters in [MW12]. The proof for the conjecture is almost completed but the proof for some cases used a different philosophy. This thesis aims to generalize Mœglin and Waldspurger’s approach to formulate a relatively uniform proof for all cases.enBranching ProblemMultiplicity TheoremNumber TheoryRepresentation TheoryThesis or Dissertation