Real characters in blocks

Abstract

We consider real versions of Brauer's $\mathrm{k}(B)$ conjecture, Olsson's conjecture and Eaton's conjecture. We prove the real version of Eaton's conjecture for $2$-blocks of groups with cyclic defect group and for the principal $2$-blocks of groups with trivial real core. We also characterize $G$-classes, real and rational $G$-classes of the defect group of$B$.