Induced representation

In mathematics, and in particular group representation theory, the induced representation is one of the major general operations for passing from a representation of a subgroup  to a representation of the (whole) group  itself. Given a representation of , the induced representation is, in a sense, the "most general" representation of that extends the given one. Since it is often easier to find representations of the smaller group than of , the operation of forming induced representations is an important tool to construct new representations.