Generalized associahedra via quiver representations

2002/05/14 by Bethany Marsh, Markus Reineke, Marsh, Bethany +3 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0205152

openalex publication_date 2002/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The main properties of these fans then become easy consequences of the known facts about tilting modules due to K. Bongartz, D. Happel and C. M. Ringel.

Cited by

• Multisets of finite intervals and a universal category of poset representations
• Derksen-Weyman-Zelevinsky mutations of infinite-dimensional modules I: Foundations

Related

• Fans and polytopes in tilting theory II: g-fans of rank 2
• APR tilting modules and graded quivers with potential
• Signed quivers, symmetric quivers, and root systems
• Polytopal realizations of generalized associahedra
• Quivers for SL(2) tilting modules