Representation theory of groups

Monomial representation

In the mathematical fields of representation theory and group theory, a linear representation ρ (rho) 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 IndHGσ. 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. (Wikipedia).

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Related pages

Finite group | Subgroup | Induced representation | Permutation representation | Coset | Group theory | Scalar (mathematics) | Image (mathematics) | Group (mathematics) | Representation theory