# The local Gan--Gross--Prasad conjecture for real unitary groups

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Hang Xue, The University of Arizona

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.