منابع مشابه
Y - systems and generalized associahedra
The goals of this paper are two-fold. First, we prove, for an arbitrary finite root system Φ, the periodicity conjecture of Al. B. Zamolodchikov [24] that concerns Y -systems, a particular class of functional relations playing an important role in the theory of thermodynamic Bethe ansatz. Algebraically, Y -systems can be viewed as families of rational functions defined by certain birational rec...
متن کاملRoot systems and generalized associahedra
Contents Root systems and generalized associahedra 1 Root systems and generalized associahedra 3 Lecture 1. Reflections and roots 5 1.1. The pentagon recurrence 5 1.2. Reflection groups 6 1.3. Symmetries of regular polytopes 8 1.4. Root systems 11 1.5. Root systems of types A, B, C, and D 13 Lecture 2. Dynkin diagrams and Coxeter groups 15 2.1. Finite type classification 15 2.2. Coxeter groups ...
متن کاملPermutahedra and Generalized Associahedra
Given a finite Coxeter system (W,S) and a Coxeter element c, or equivalently an orientation of the Coxeter graph of W , we construct a simple polytope whose outer normal fan is N. Reading’s Cambrian fan Fc, settling a conjecture of Reading that this is possible. We call this polytope the c-generalized associahedron. Our approach generalizes Loday’s realization of the associahedron (a type A c-g...
متن کاملGeneralized Associahedra via Quiver Representations
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.
متن کاملVertex Barycenter of Generalized Associahedra
We show that the vertex barycenter of generalized associahedra and permutahedra coincide for any finite Coxeter system.
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2003
ISSN: 0003-486X
DOI: 10.4007/annals.2003.158.977