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

Abstract

In this paper, we define compact open subgroups of quasi-split even unitary groups for each even non-negative integers, and establish the theory of local newforms for irreducible tempered generic representations with a certain condition on the central characters. To do this, we use the local Gan-Gross-Prasad conjecture, the local Rankin-Selberg integrals, and the local theta correspondence.