Supercharacter theory via the group determinant

2020/03/28 by Burkett, Shawn T.
#20C15 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2003.12695

Abstract

Ferdinand Georg Frobenius is generally considered the creator of character theory of finite groups. This achievement came from the study of the group determinant, which is the determinant of a matrix coming from the regular representation. In this paper, we generalize several of Frobenius' results about the group determinant and use them find a new formulation of supercharacter theory in terms of factorizations of the group determinant.

Related

• The structure of normal lattice supercharacter theories
• Construction of supercharacter theories of finite groups
• Generalization of Frobenius' theorem for group determinants
• supercharacter table of certain finite groups
• Supercharacter formulas for pattern groups