  We start the systematic study of extended Weyl groups, and continue the
combinatorial description of thick subcategories in hereditary categories
started by Ingalls-Thomas, Igusa-Schiffler-Thomas and Krause. We show that for
a weighted projective line $\mathbb{X}$ there exists an order preserving
bijection between the thick subcategories of $\mathrm{coh}(\mathbb{X})$
generated by an exceptional sequence and a subposet of the interval poset of a
Coxeter transformation $c$ in the Weyl group of a simply-laced extended root
system if the Hurwitz action is transitive on the reduced reflection
factorizations of $c$ that generate the Weyl group. By using combinatorial and
group theoretical tools we show that this assumption on the transitivity of the
Hurwitz action is fulfilled for a weighted projective line $\mathbb{X}$ of
tubular type.

Representation Theory;Combinatorics;Group Theory