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 genera...

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Bibliographic Details
Published in:arXiv.org 2016-03
Main Authors: Nakamura, Shunsuke, Shiraishi, Yuuki, Takahashi, Atsushi
Format: Article
Language:English
Subjects:
Isomorphism
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Summary: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.
ISSN:2331-8422