  A general method for computing irreducible representations of Weyl groups and
Iwahori-Hecke algebras was introduced earlier by the first author. The
representations of the algebras of types $A_n$, $B_n$, $D_n$ and $G_2$ were
computed and it is the purpose of this paper to extend these computations to
$F_4$. The main goal here is to compute irreducible representations of the
Iwahori-Hecke algebra of type $F_4$ by only using information in the character
table of the Weyl group.
