This is a question regarding a seemingly unexplained notation in Curtis–Reiner: Methods of Representation Theory, volume 1. In subsection §09D on the character table, on page 215, between equations (9.28) and (9.29), the notation $\mathbf Z_m(C_i)$ is used, but as far as I can tell, $\mathbf Z_m$ was never introduced. Could someone please explain to me what it means?
The following definition has been suggested to me. Consider the action of $G$ on $Z_m$; this yields a representation $G\to\mathrm{GL}_{z_m}(K)$. Then $\mathbf Z_m$ is the $K$-linear extension $KG\to M_{z_m}(K)$. This indeed makes the paragraph cited above make sense.