Representation stability for sequences of 0-Hecke modules
Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 619-661.

We define a new category analogous to FI for the 0-Hecke algebra H n (0) called the 0-Hecke category, , indexing sequences of representations of H n (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 -module. We then provide examples of -modules and discuss further desirable properties these modules possess.

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DOI: 10.5802/alco.172
Classification: 13A50, 13C05, 16P40
Keywords: Representation stability, Diagram algebra, Hecke algebra
Laudone, Robert P. 1

1 University of Michigan Dept. of mathematics 530 Church St. Ann Arbor MI 48109, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Laudone, Robert P. Representation stability for sequences of 0-Hecke modules. Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 619-661. doi : 10.5802/alco.172. https://alco.centre-mersenne.org/articles/10.5802/alco.172/

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