We prove a smooth transfer statement analogous to Jacquet-Rallis's fundamental lemma, use it to compute a local spherical character appearing in the Ichino-Ikeda conjecture, and prove a statement on the existence of local newforms for unitary groups as a corollary.
Local newforms for generic representations of unramified even unitary groups I: Even conductor case
On local newforms for unramified U(2,1)
Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups
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