A Cambrian framework for the oriented cycle
Abstrak
This paper completes the project of constructing combinatorial models (called frameworks) for the exchange graph and g-vector fan associated to any exchange matrix B whose Cartan companion is of finite or affine type, using the combinatorics and geometry of Coxeter-sortable elements and Cambrian lattices/fans. Specifically, we construct a framework in the unique non-acyclic affine case, the cyclically oriented n-cycle. In the acyclic affine case, a framework was constructed by combining a copy of the Cambrian fan for B with an antipodal copy of the Cambrian fan for -B. In this paper, we extend this "doubled Cambrian fan" construction to the oriented n-cycle, using a more general notion of sortable elements for quivers with cycles.
Topik & Kata Kunci
Penulis (2)
Nathan Reading
David E. Speyer
Akses Cepat
- Tahun Terbit
- 2015
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓