2005/11/15 by Bin Zhu, Zhu, Bin
Mathematics · #16G20 #16G70 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.math/0511380
openalex publication_date 2005/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the "truncated simple reflections" on the set of almost positive roots Φ≥ -1 associated to a finite dimensional semisimple Lie algebra. Combining with the tilting theory in cluster categories developed in [4], we give a unified interpretation via quiver representations for the generalized associahedra associated to the root systems of all Dynkin types (a simply-laced or non-simply-laced). This confirms the conjecture 9.1 in [4] in all Dynkin types.