THE <i>p</i> -RATIONALITY OF HEIGHT-ZERO CHARACTERS

Abstract We propose and present evidence for a conjectural global-local phenomenon concerning the p -rationality of height-zero characters. Specifically, if $\chi $ is a height-zero character of a finite group G and D is a defect group of the p -block of G containing $\chi $ , then the p -rationality of $\chi $ can be captured inside the normalizer ${\mathbf {N}}_G(D)$ .