Monomial representation

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

• Hazewinkel, Michiel, ed. (2001) [1994], "Monomial representation", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4