On simply-laced generalized root systems
  We show the uniqueness and existence of the Euler form for a simply-laced generalized root system. This enables us to show that the Coxeter element for a simply-laced generalized root system is admissible in the sense of R.~W.~Carter. As an application, the isomorphism classes of simply-laced generalized root systems with positive definite Cartan forms are classified by Cartar's admissible diagrams associated to their Coxeter elements. 
Shunsuke Nakamura, Yuuki Shiraishi, Atsushi Takahashi
math.AG math.RT