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Let G be the unramified unitary group in three variables defined over ap-adic field F of odd residual characteristic. In this paper, we investigatelocal newforms for irreducible admissible representations of G. We introduce afamily of open compact subgroups {K_n} of G to define the local newforms forrepresentations of G as the K_n-fixed vectors. We prove the existence of localnewforms for generic representations and the multiplicity one property of thelocal newforms for admissible representations.

On local newforms for unramified U(2,1)