A classical branching theorem of Weyl describes how an irreducible representation of compact U(n+1) decomposes when restricted to U(n). The local Gan-Gross-Prasad conjecture provides a conjectural extension to the setting of representations of noncompact unitary groups lying in a generic L-packet. We prove this conjecture. Previously Beuzart-Plessis proved the “multiplicity one in a Vogan packet” part of the conjecture for tempered L-packets using the local trace formula approach initiated by Waldspurger. Our proof uses theta lifts instead, and is independent of the trace formula argument.
This video is part of the Institute for Advanced Study‘s Number theory seminar.
