Cambrian frameworks for cluster algebras of affine type
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- by Nathan Reading and David E. Speyer PDF
- Trans. Amer. Math. Soc. 370 (2018), 1429-1468
Abstract:
We give a combinatorial model for the exchange graph and $\mathbf {g}$-vector fan associated to any acyclic exchange matrix $B$ of affine type. More specifically, we construct a reflection framework for $B$ in the sense of [N. Reading and D. E. Speyer, “Combinatorial frameworks for cluster algebras”] and establish good properties of this framework. The framework (and in particular the $\mathbf {g}$-vector fan) is constructed by combining a copy of the Cambrian fan for $B$ with an antipodal copy of the Cambrian fan for $-B$.References
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Additional Information
- Nathan Reading
- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
- MR Author ID: 643756
- Email: reading@math.ncsu.edu
- David E. Speyer
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
- MR Author ID: 663211
- Email: speyer@umich.edu
- Received by editor(s): December 30, 2015
- Received by editor(s) in revised form: January 23, 2017
- Published electronically: September 15, 2017
- Additional Notes: The first author was partially supported by NSA grant H98230-09-1-0056, by Simons Foundation grant #209288, and by NSF grant DMS-1101568. The second author was supported in part by a Clay Research Fellowship and by NSF grant DMS-1600223.
- © Copyright 2017 by Nathan Reading and David E. Speyer
- Journal: Trans. Amer. Math. Soc. 370 (2018), 1429-1468
- MSC (2010): Primary 13F60, 20F55
- DOI: https://doi.org/10.1090/tran/7193
- MathSciNet review: 3729507