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Let $F$ be a non-archimedean local field of residue characteristic $p$, $G$be the group $GL(n, F)$. In this note, under the assumption $(n, p)=1$, we showa simple cuspidal representation $\pi$ (that with normalized level$\frac{1}{n}$) of $G$ is determined uniquely up to isomorphism by the localconstants of $\chi\circ \text{det}\otimes \pi$ for all characters $\chi$ of$F^\times$.

A remark on the simple cuspidal representations of GL(n, F)