# ALGEBRAIC COMBINATORICS

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 $\mathbf{FI}$ for the $0$-Hecke algebra ${H}_{n}\left(0\right)$ called the $0$-Hecke category, $ℋ$, indexing sequences of representations of ${H}_{n}\left(0\right)$ 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.

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.172
Classification: 13A50,  13C05,  16P40
Keywords: Representation stability, Diagram algebra, Hecke algebra
@article{ALCO_2021__4_4_619_0,
author = {Laudone, Robert P.},
title = {Representation stability for sequences of {0-Hecke} modules},
journal = {Algebraic Combinatorics},
pages = {619--661},
publisher = {MathOA foundation},
volume = {4},
number = {4},
year = {2021},
doi = {10.5802/alco.172},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.172/}
}
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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