Shawn T. Burkett
Published 2020-03-28Version 1
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.
Generalization of Frobenius' theorem for group determinants
Rational representations and permutation representations of finite groups
Growth Problems for Representations of Finite Groups
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