Abstract
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 Following the approach of C. Mœglin and J.-L. Waldspurger,
 this article proves the local Gross–Prasad conjecture over
 
 and
 
 based
 on the tempered cases of Luo and the author.
  
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              Keywords
              
                local Gross–Prasad conjecture, branching problem,
                multiplicity formula
               
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              Mathematical Subject Classification
              
                Primary: 22E50, 22E45
               
              
                Secondary: 20G20
               
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              Milestones
              
                Received: 25 November 2022
               
              
                Revised: 24 August 2025
               
              
                Accepted: 25 August 2025
               
              
                Published: 1 September 2025
               
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