Super-Brauer characters and super-regular classes

摘要

Persi Diaconis and I. M. Isaacs generalized the character theory to super-character theories for an arbitrary finite group (Diaconis and Isaacs, in Trans Am Math Soc 360(5):2359–2392, 2008). In these theories, the irreducible characters are replaced by certain so-called supercharacters, and the conjugacy classes of the group are replaced by superclasses. Also, Diaconis and Isaacs discussed supercharacter theories and gave some properties of them. We consider in this note certain sums of irreducible Brauer characters and compatible unions of regular conjugacy classes in an arbitrary finite group and we give a generalization of the Brauer character theory to super-Brauer character theories. We also discuss super-Brauer character theories and obtain some results which are similar to those of Diaconis and Isaacs.