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Let p be a prime number. We classify all smooth irreducible mod-prepresentations of the unramified unitary group U(1,1)(Q_p^2/Q_p) in twovariables. We then investigate Langlands parameters in characteristic passociated to U(1,1)(Q_p^2/Q_p), and propose a correspondence between certainequivalence classes of Langlands parameters and certain isomorphism classes ofsemisimple L-packets on U(1,1)(Q_p^2/Q_p).

A classification of the irreducible mod-p representations of U(1,1)(Q_p^2/Q_p)