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