The structure of normal lattice supercharacter theories
Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1059-1078.

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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DOI: 10.5802/alco.126
Classification: 05E10,  20C15,  20E15
Keywords: Supercharacters, distributive lattices, restriction functor, tensor products.
Aliniaeifard, Farid 1; Thiem, Nathaniel 2

1 The University of British Columbia Department of Mathematics 1984 Mathematics Road Vancouver BC V6T 1Z2 Canada
2 University of Colorado Department of Mathematics UCB 395 Boulder CO 80309, USA
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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] Aliniaeifard, Farid Normal supercharacter theories and their supercharacters, J. Algebra, Volume 469 (2017), pp. 464-484 | Article | MR: 3563023 | Zbl: 06642849

[2] Aliniaeifard, Farid; Thiem, Nathaniel Pattern groups and a poset based Hopf monoid, J. Combin. Theory Ser. A, Volume 172 (2020), Paper no. 105187, 31 pages | Article | MR: 4046316 | Zbl: 07172396

[3] Andrews, Scott The Hopf monoid on nonnesting supercharacters of pattern groups, J. Algebraic Combin., Volume 42 (2015) no. 1, pp. 129-164 | Article | MR: 3365596 | Zbl: 1365.20005

[4] Bergeron, Nantel; Thiem, Nathaniel A supercharacter table decomposition via power-sum symmetric functions, Internat. J. Algebra Comput., Volume 23 (2013) no. 4, pp. 763-778 | Article | MR: 3078055 | Zbl: 1283.20004

[5] Burkett, Shawn Subnormality and Normal Series in Supercharacter Theory, ProQuest LLC, Ann Arbor, MI, 2018, 139 pages Thesis (Ph.D.)–University of Colorado at Boulder | MR: 3876513

[6] Burkett, Shawn; Lamar, Jonathan; Lewis, Mark L.; Wynn, Casey Groups with exactly two supercharacter theories, Comm. Algebra, Volume 45 (2017) no. 3, pp. 977-982 | Article | MR: 3573353 | Zbl: 1369.20005

[7] Fowler, Christopher F.; Garcia, Stephan Ramon; Karaali, Gizem Ramanujan sums as supercharacters, Ramanujan J., Volume 35 (2014) no. 2, pp. 205-241 | Article | MR: 3266478 | Zbl: 1368.11090

[8] Marberg, Eric A supercharacter analogue for normality, J. Algebra, Volume 332 (2011), pp. 334-365 | Article | MR: 2774691 | Zbl: 1243.20011

[9] Yan, Ning 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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