 Induced character

For a character $\psi$ of $H\le G$, the induced character isThis is the character of a representation of $\mathbb{C}[G]{\otimes }_{\mathbb{C}[H]}{V}_{\psi }$. Substituting this expression into the character inner product and putting $g=xh{x}^{-1}$ proves Frobenius reciprocity.

Induced characters refer to representations of a group that arise from the representation of a subgroup. In the context of representation theory—an area of mathematics that studies abstract algebraic structures through linear transformations—induced characters are a way to construct new representations of a group via a subgroup.