Tree modules and counting polynomials
arXiv:1112.4782 · doi:10.1007/s10468-012-9359-x
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.
11 pages, comments welcomed, v2: improvements in exposition and some details added to last section