  Let F be a non-Archimedean local field and let E be an unramified extension
of F of degree n>1. To each sufficiently generic multiplicative character of E
(the details are explained in the body of the paper) one can associate an
irreducible n-dimensional representation of the Weil group W_F of F, which
corresponds to an irreducible supercuspidal representation \pi\ of GL_n(F) via
the local Langlands correspondence. In turn, via the Jacquet-Langlands
correspondence, \pi\ corresponds to an irreducible representation \rho\ of the
multiplicative group of the central division algebra over F with invariant 1/n.
In this note we give a new geometric construction of the representations \pi\
and \rho, which is simpler than the existing algebraic approaches (in
particular, the use of the Weil representation over finite fields is
eliminated).
