Monomial representation
In the mathematical fields of representation theory and group theory, a linear representation ρ {\displaystyle \rho } (rho) of a group G {\displaystyle G} is a monomial representation if there is a finite-index subgroup H {\displaystyle H} and a one-dimensional linear representation σ {\displaystyle \sigma } of H {\displaystyle H} , such that ρ {\displaystyle \rho } is equivalent to the induced representation I n d H G σ {\displaystyle \mathrm {Ind} _{H}^{G_{\sigma }}} . Alternatively, one may define it as a representation whose image is in the monomial matrices.