We construct Hopf algebras whose elements are representations of combinatorial automorphism groups, by generalising a theorem of Zelevinsky on Hopf algebras of representations of wreath products. As an application we attach symmetric functions to representations of graph automorphism groups, generalising and refining Stanley’s chromatic symmetric function.
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Keywords: Combinatorial Hopf algebra, PSH algebra, wreath product, chromatic symmetric function
Crisp, Tyrone 1; Hill, Caleb Kennedy 1
CC-BY 4.0
@article{ALCO_2022__5_1_93_0,
author = {Crisp, Tyrone and Hill, Caleb Kennedy},
title = {Combinatorial {Hopf} algebras from representations of families of wreath products},
journal = {Algebraic Combinatorics},
pages = {93--120},
publisher = {MathOA foundation},
volume = {5},
number = {1},
year = {2022},
doi = {10.5802/alco.198},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.198/}
}
TY - JOUR AU - Crisp, Tyrone AU - Hill, Caleb Kennedy TI - Combinatorial Hopf algebras from representations of families of wreath products JO - Algebraic Combinatorics PY - 2022 SP - 93 EP - 120 VL - 5 IS - 1 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.198/ DO - 10.5802/alco.198 LA - en ID - ALCO_2022__5_1_93_0 ER -
%0 Journal Article %A Crisp, Tyrone %A Hill, Caleb Kennedy %T Combinatorial Hopf algebras from representations of families of wreath products %J Algebraic Combinatorics %D 2022 %P 93-120 %V 5 %N 1 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.198/ %R 10.5802/alco.198 %G en %F ALCO_2022__5_1_93_0
Crisp, Tyrone; Hill, Caleb Kennedy. Combinatorial Hopf algebras from representations of families of wreath products. Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 93-120. doi : 10.5802/alco.198. https://alco.centre-mersenne.org/articles/10.5802/alco.198/
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