On the equivalence of two stability conditions of FB-modules

Publication date: 13 July 2018

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.

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory of groups (20Cxx)

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