Supercharacter theories and Schur rings

2010/06/07 by Anders O. F. Hendrickson, Hendrickson, Anders O. F. · 1 citation
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Finite Group Theory Research #math.GR #math.RT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1006.1363

This is reworked from "Constructions of supercharacter theories," arXiv:0905.3538v1 [math.GR], including new material on Schur rings and on superinduction

arxiv created 2010/06/07 · arxiv updated 2010/06/09

Abstract

Diaconis and Isaacs have defined the supercharacter theories of a finite group to be certain approximations to the ordinary character theory of the group. We make explicit the connection between supercharacter theories and Schur rings, and we provide supercharacter theory constructions which correspond to Schur ring constructions of Leung and Man and of Tamaschke.

Citations

• Construction of supercharacter theories of finite groups

Cited by

• An Enumeration of the Supercharacter Theories of C_p × C₂ × C₂ for Prime p

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