Editing Induced representation (section)

{{Short description|Process of extending a representation of a subgroup to the parent group}}

In [[group theory]], the '''induced representation''' is a [[group representation|representation of a group]], {{mvar|G}}, which is constructed using a known representation of a [[subgroup]] {{mvar|H}}. Given a representation of {{mvar|H}}'','' the induced representation is, in a sense, the "most general" representation of {{mvar|G}} that extends the given one. Since it is often easier to find representations of the smaller group {{mvar|H}} than of {{mvar|G}}'','' the operation of forming induced representations is an important tool to construct new representations''.''

Induced representations were initially defined by [[Ferdinand Georg Frobenius|Frobenius]], for [[linear representation]]s of [[finite group]]s. The idea is by no means limited to the case of finite groups, but the theory in that case is particularly well-behaved.