We define a new category analogous to for the -Hecke algebra called the -Hecke category, , indexing sequences of representations of as 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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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 = {http://www.numdam.org/articles/10.5802/alco.172/} }
TY - JOUR AU - Laudone, Robert P. TI - Representation stability for sequences of 0-Hecke modules JO - Algebraic Combinatorics PY - 2021 SP - 619 EP - 661 VL - 4 IS - 4 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.172/ DO - 10.5802/alco.172 LA - en ID - ALCO_2021__4_4_619_0 ER -
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. http://www.numdam.org/articles/10.5802/alco.172/
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