The character theory of finite groups has numerous basic questions that are often already quite involved: enumeration of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between groups. A supercharacter theory is a framework for simplifying the character theory of a finite group, while ideally not losing all the important information. This paper studies one such theory that straddles the gap between retaining valuable group information while reducing the above fundamental questions to more combinatorial lattice constructions.

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Accepted:

Published online:

Keywords: Supercharacters, distributive lattices, restriction functor, tensor products.

^{1}; Thiem, Nathaniel

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@article{ALCO_2020__3_5_1059_0, author = {Aliniaeifard, Farid and Thiem, Nathaniel}, title = {The structure of normal lattice supercharacter theories}, journal = {Algebraic Combinatorics}, pages = {1059--1078}, publisher = {MathOA foundation}, volume = {3}, number = {5}, year = {2020}, doi = {10.5802/alco.126}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.126/} }

TY - JOUR AU - Aliniaeifard, Farid AU - Thiem, Nathaniel TI - The structure of normal lattice supercharacter theories JO - Algebraic Combinatorics PY - 2020 SP - 1059 EP - 1078 VL - 3 IS - 5 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.126/ UR - https://doi.org/10.5802/alco.126 DO - 10.5802/alco.126 LA - en ID - ALCO_2020__3_5_1059_0 ER -

Aliniaeifard, Farid; Thiem, Nathaniel. The structure of normal lattice supercharacter theories. Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1059-1078. doi : 10.5802/alco.126. https://alco.centre-mersenne.org/articles/10.5802/alco.126/

[1] Normal supercharacter theories and their supercharacters, J. Algebra, Volume 469 (2017), pp. 464-484 | DOI | MR | Zbl

[2] Pattern groups and a poset based Hopf monoid, J. Combin. Theory Ser. A, Volume 172 (2020), Paper no. 105187, 31 pages | DOI | MR | Zbl

[3] The Hopf monoid on nonnesting supercharacters of pattern groups, J. Algebraic Combin., Volume 42 (2015) no. 1, pp. 129-164 | DOI | MR | Zbl

[4] A supercharacter table decomposition via power-sum symmetric functions, Internat. J. Algebra Comput., Volume 23 (2013) no. 4, pp. 763-778 | DOI | MR | Zbl

[5] Subnormality and Normal Series in Supercharacter Theory, ProQuest LLC, Ann Arbor, MI, 2018, 139 pages Thesis (Ph.D.)â€“University of Colorado at Boulder | MR

[6] Groups with exactly two supercharacter theories, Comm. Algebra, Volume 45 (2017) no. 3, pp. 977-982 | DOI | MR | Zbl

[7] Ramanujan sums as supercharacters, Ramanujan J., Volume 35 (2014) no. 2, pp. 205-241 | DOI | MR | Zbl

[8] A supercharacter analogue for normality, J. Algebra, Volume 332 (2011), pp. 334-365 | DOI | MR | Zbl

[9] Representations of finite unipotent linear groups by the method of clusters (2010) (Preprint available at http://arxiv.org/abs/1004.2674)

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