Gan-Gross-Prasad Conjecture for U(p,q)

In this paper, we give a proof of the Gan-Gross-Prasad conjecture for the discrete series of U(p,q). Given a discrete series representation $D(λ)$ in terms of the Harish-Chandra parameter, the restriction of $D(λ)$ to U(p-1,q) contains $D(μ)$ as a subrepresentation if and only if $λ$ and $μ$ interlaces in a very special way.

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