English

Generalized Reflection Root Systems

Representation Theory 2017-09-26 v1

Abstract

We study a combinatorial object, which we call a GRRS (generalized reflection root system); the classical root systems and GRSs introduced by V. Serganova are examples of finite GRRSs. A GRRS is finite if it contains a finite number of vectors and is called affine if it is infinite and has a finite minimal quotient. We prove that an irreducible GRRS containing an isotropic root is either finite or affine; we describe all finite and affine GRRSs and classify them in most of the cases.

Keywords

Cite

@article{arxiv.1507.08819,
  title  = {Generalized Reflection Root Systems},
  author = {Maria Gorelik and Ary Shaviv},
  journal= {arXiv preprint arXiv:1507.08819},
  year   = {2017}
}

Comments

27 pages

R2 v1 2026-06-22T10:23:15.698Z