On simply-laced generalized root systems
Algebraic Geometry
2016-03-28 v1 Representation Theory
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.
Cite
@article{arxiv.1603.07821,
title = {On simply-laced generalized root systems},
author = {Shunsuke Nakamura and Yuuki Shiraishi and Atsushi Takahashi},
journal= {arXiv preprint arXiv:1603.07821},
year = {2016}
}
Comments
20 pages