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Abstract: In the present paper we determine the representation type of the 0-Hecke algebra of a finite Coxeter group.

By using the Ringel-Hall algebra approach we first present a new proof of Kac's theorem for species over a finite field. The method used here is quite different from earlier techniques. In [SV] Sevenhant and Van den Bergh have discovered an interesting relation between a conjecture of Kac on representations of quivers and the structure of the Ringel-Hall algebras in some special cases. We second show that this relation still holds for species.

In this article we determine the pairs of posets which are finitely represented.