ALGEBRAIC COMBINATORICS

no. 5
The structure of normal lattice supercharacter theories
Aliniaeifard, Farid1; Thiem, Nathaniel2
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
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.

Received:
Revised:
Accepted:
Published online:
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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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/

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