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arXiv · 1603.07821

On simply-laced generalized root systems

Shunsuke Nakamura·Yuuki Shiraishi·Atsushi Takahashi
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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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Shunsuke Nakamura, Yuuki Shiraishi, Atsushi Takahashi. 2016-03-25. On simply-laced generalized root systems. https://arxiv.org/abs/1603.07821

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