English

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.

Keywords

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

R2 v1 2026-06-22T13:18:29.934Z