This dissertation investigates the local Gan-Gross-Prasad conjecture for tempered representations of Gan-Gross-Prasad (GGP) triples associated with general spin groups, extending previous work by Waldspurger for special orthogonal groups and Beuzart-Plessis for unitary groups. We follow the structural framework developed for the unitary case to address both p-adic and Archimedean settings, utilizing the similarities in the root systems and Levi subgroup decompositions of general spin and special orthogonal groups. The primary result establishes a multiplicity-one theorem for the GGP triples. To achieve this, we derive a local trace formula that connects the multiplicity formula with spectral and geometric expansions of a certain distribution.
Samantha Artemis Pease (Thu,) studied this question.