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# 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}^{G}σ.

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), "Monomial representation",
*Encyclopedia of Mathematics*, Springer, ISBN 978-1-55608-010-4

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