Root systems constructed by folding of the extended Dynkin diagrams

The extended affine Weyl group of a root system is the semidirect product of the corresponding Weyl group by its coweight lattice. The stabilizer subgroup of the extended affine Weyl group with respect to the corresponding fundamental alcove induces a subgroup of automorphisms of the extended Dynkin diagram. In this paper, we construct a finite root system by folding by the elements of the subgroup.