A CLASSIFICATION OF THE IRREDUCIBLE MOD-p REPRESENTATIONS OF U(1,1)(Qp2/Qp)

Let p be a prime number. We classify all smooth irreducible mod-p representations of the unramified unitary group U(1, 1)(Q(2)/Q(p)) in two variables. We then investigate Langlands parameters in characteristic p associated to U(1, 1)(Q(p2)/Q(p)), and propose a correspondence between certain equivalence classes of Langlands parameters and certain isomorphism classes of semisimple L-packets on U(1, 1) (Q(p2)/Q(p)).