Tree modules and counting polynomials
Representation Theory
2013-09-24 v2
Abstract
We give a formula for counting tree modules for the quiver S_g with g loops and one vertex in terms of tree modules on its universal cover. This formula, along with work of Helleloid and Rodriguez-Villegas, is used to show that the number of d-dimensional tree modules for S_g is polynomial in g with the same degree and leading coefficient as the counting polynomial A_{S_g}(d, q) for absolutely indecomposables over F_q, evaluated at q=1.
Keywords
Cite
@article{arxiv.1112.4782,
title = {Tree modules and counting polynomials},
author = {Ryan Kinser},
journal= {arXiv preprint arXiv:1112.4782},
year = {2013}
}
Comments
11 pages, comments welcomed, v2: improvements in exposition and some details added to last section