1. References

In mathematics, a linear representation ρ of a group G is a monomial representation if there is a finite-index subgroup H and a one-dimensional linear representation σ of H, such that ρ is equivalent to the induced representation

Ind_H^Gσ.

Alternatively, one may define it as a representation whose image is in the monomial matrices.

Here for example G and H may be finite groups, so that induced representation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of G on the cosets of H. It is necessary only to keep track of scalars coming from σ applied to elements of H.

References

• {{Springer|id=Monomial_representation|title=Monomial representation}}

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