Root systems and generalized associahedra
Combinatorics
2026-05-13 v3 Rings and Algebras
Representation Theory
Abstract
These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of root systems, generalized associahedra, and the combinatorics of clusters. Lectures 1-2 cover classical material: root systems, finite reflection groups, and the Cartan-Killing classification. Lectures 3-4 provide an introduction to cluster algebras from a combinatorial perspective. Lecture 5 is devoted to related topics in enumerative combinatorics.
Keywords
Cite
@article{arxiv.math/0505518,
title = {Root systems and generalized associahedra},
author = {Sergey Fomin and Nathan Reading},
journal= {arXiv preprint arXiv:math/0505518},
year = {2026}
}
Comments
69 pages, many figures. Version 3 is the final version appearing in the PCMI Lecture Series volume.