Representation stability for sequences of 0-Hecke modules
Abstract
We define a new category analogous to FI for the 0-Hecke algebra Hn(0) called the 0-Hecke category, H, indexing sequences of representations of Hn(0) as n varies under suitable compatibility conditions. We establish a new type of representation stability in this setting and prove it is implied by being a finitely generated H-module. We then provide examples of H-modules and discuss further desirable properties these modules possess.
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