On simply-laced generalized root systems

2016/03/25 by Nakamura, Shunsuke, Shiraishi, Yuuki, Takahashi, Atsushi
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1603.07821

Abstract

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.

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