Bessel models for real unitary groups: the tempered case (Q6046457)

In the paper under the review, the author proves the local Gan-Gross-Prasad conjecture for all tempered \(L\)-packets of real unitary groups \(U(n+2t+1) \times U(n)\). Roughly, this conjecture states that in each Vogan packet of \(U(n+1) \times U(n)\) exists a unique ordered pair \((\pi, \sigma)\), consisting of an irreducible representation \(\pi\) of \(U(n+1)\) and an irreducible representation \(\sigma\) of \(U(n)\) such that \(\mathrm{Hom}_{U(W)}(\pi \widehat{\otimes} \sigma) \neq 0\), and that this ordered pair can be specified using the local root numbers. The proof happens to be rather simple and is based on the exploration of the theta lifts. It does not reduce the tempered case to the square-integrable one, and it specifies to real unitary groups.