  Let $W$ be a finite Weyl group of classical type which may not be
irreducible, $F$ an algebraically closed field, $q$ an invertible element of
$F$. We denote by $\mathcal H_W(q)$ the associated Hecke algebra. If $q=1$ then
it is $FW$ and we know the representation type. Thus, we assume that $q\ne 1$.
Let $P_W(x)$ be the Poincare polynomial of $W$. It is well-known that $\mathcal
H_W(q)$ is semisimple if and only if $x-q$ does not divide $P_W(x)$. We show
that the similar results hold for finiteness, tameness and wildness. In other
words, the Poincare polynomial governs the representation type of $\mathcal
H_W(q)$ completely. Note that the finiteness result was already given in the
author's previous papers, some of which were written with Andrew Mathas.
  The proof uses the Fock space theory, which was developed for proving the LLT
conjecture (see AMS Univ. Lec. Ser. 26), the Specht module theory, which was
developed by Dipper, James and Murphy in this case, and results from the theory
of finite dimensional algebras.
