On the equivalence of two stability conditions of FB-modules
Representation Theory
2018-07-18 v2
Abstract
We give a proof of the fact that for an FB-module the properties of being "representation stable" (RS) and "having a polynomial character" (PC) are equivalent. We obtain optimal estimates for the gap between the ranks of the polynomiality and of representation stability. As a by-product, we show that the degree of the polynomial character and the weight at infinity of an FB-module coincide, which we apply to determine the weight at infinity of a tensor product of FB-modules.
Keywords
Cite
@article{arxiv.1807.05032,
title = {On the equivalence of two stability conditions of FB-modules},
author = {Alberto Arabia},
journal= {arXiv preprint arXiv:1807.05032},
year = {2018}
}
Comments
em 25 pages, 2 figures