Combinatorics of $F$-polynomials
Representation Theory
2021-08-04 v3 Combinatorics
Abstract
We use the stabilization functors to study the combinatorial aspects of the -polynomial of a representation of any finite-dimensional basic algebra. We characterize the vertices of their Newton polytopes. We give an explicit formula for the -polynomial restricting to any face of its Newton polytope. For acyclic quivers, we give a complete description of all facets of the Newton polytope when the representation is general. We also prove that the support of the -polynomial is saturated for any rigid representation. We provide many examples and counterexamples, and pose several conjectures.
Cite
@article{arxiv.1909.10151,
title = {Combinatorics of $F$-polynomials},
author = {Jiarui Fei},
journal= {arXiv preprint arXiv:1909.10151},
year = {2021}
}
Comments
25 pages; V2. modification according to arXiv:1911.10513; V3. various corrections and modifications thanks to the referee's great effort