  Let E be a finite extension of Fp. Using Fontaine's theory of
(phi,Gamma)-modules, Colmez has shown how to attach to any irreducible E-linear
representation of Gal(Qpbar/Qp) an infinite dimensional smooth irreducible
E-linear representation of B_2(Qp) that has a central character. We prove that
every such representation of B_2(Qp) arises in this way.
  Our proof extends to algebraically closed fields E of characteristic p. In
this case, infinite dimensional smooth irreducible E-linear representations of
B_2(Qp) having a central character arise in a similar way from irreducible
E-linear representations of the Weil group of Qp.
