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In this paper, we define compact open subgroups of quasi-split even unitarygroups for each even non-negative integers, and establish the theory of localnewforms for irreducible tempered generic representations with a certaincondition on the central characters. To do this, we use the localGan-Gross-Prasad conjecture, the local Rankin-Selberg integrals, and the localtheta correspondence.

Local newforms for generic representations of unramified even unitary groups I: Even conductor case