  We construct a full strongly exceptional collection in the triangulated
category of graded matrix factorizations of a polynomial associated to a
non-degenerate regular system of weights whose smallest exponents are equal to
-1. In the associated Grothendieck group, the strongly exceptional collection
defines a root basis of a generalized root system of sign (l,0,2) and a Coxeter
element of finite order, whose primitive eigenvector is a regular element in
the expanded symmetric domain of type IV with respect to the Weyl group.
