Projective supercharacter theory. Issue 8 (2nd August 2020) - Finnegan, C.; Higgs, R. J.
Abstract: The idea of supercharacters for ordinary characters of a finite group G was introduced by Diaconis and Isaacs and further extended to Brauer characters by Chen and Lewis. The twin concepts of supercharacters and superclasses are further extended here to α -characters of G for α a complex-valued 2-cocycle of G . An α -quasi-supercharacter theory of G arises when the set of α -quasi-supercharacters of G are compatible with the set of α -regular quasi-superclasses of G . The structure of solvable groups that have exactly two α -quasi-supercharacter theories is determined. Communicated by Mark L. Lewis