On local newforms for unramified U(2,1)

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Let G be the unramified unitary group in three variables defined over a p-adic field F of odd residual characteristic. In this paper, we investigate local newforms for irreducible admissible representations of G. We introduce a family of open compact subgroups Kₙ of G to define the local newforms for representations of G as the Kₙ-fixed vectors. We prove the existence of local newforms for generic representations and the multiplicity one property of the local newforms for admissible representations.