---
title: Induced Representations
description: Induced representation is a method for constructing a representation of a group from a known representation of one of its subgroups. Learners will understand Frobenius reciprocity, Mackey's theorem, and how to analyze representations of larger algebraic structures.
category: mathematics
subcategory: representation-theory
difficulty: beginner, intermediate, advanced
url: /subject/induced-representations
---

# Induced Representations

Induced representation is a method for constructing a representation of a group from a known representation of one of its subgroups. Learners will understand Frobenius reciprocity, Mackey's theorem, and how to analyze representations of larger algebraic structures.

## Available Resources

1 Courses • 4 Websites

## Websites

### 1. Groupprops: Induced Representation

Groupprops wiki reference entry defining the induced representation abstractly as a function space and explicitly as block monomial matrices over a coset transversal, with listed facts on transitivity of induction, induced characters, Frobenius reciprocity and permutation representations.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://groupprops.subwiki.org/wiki/Induced_representation

**Tags:** representation-theory, induced-representations, finite-groups, frobenius-reciprocity, character-theory

### 2. nLab: Induced Representation

nLab entry treating induced and co-induced representations as the left and right adjoints of restriction to a subgroup, derived via group algebras and via groupoids, with Frobenius reciprocity as the adjunction and links to Hecke algebras and Zuckerman functors.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://ncatlab.org/nlab/show/induced+representation

**Tags:** representation-theory, induced-representations, category-theory, adjoint-functors, frobenius-reciprocity

### 3. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

### 4. nLab

Collaborative wiki for mathematics, physics and philosophy written from a category-theoretic viewpoint, with cross-linked entries on categories, functors, adjunctions, topos theory, higher category theory and homotopy theory. Readers can look up precise definitions, examples and references for advanced structural mathematics.

**Difficulty:** Advanced | **Language:** English | **Price:** Free

**Link:** https://ncatlab.org

**Tags:** category-theory, higher-category-theory, topos-theory, homotopy-theory, reference-wiki

## Courses

### 1. Representation Theory of Finite Groups

Learn induced representations within the representation theory of finite groups with this course by Richard Borcherds.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.youtube.com/playlist?list=PLn6dA-hP_G8TTniGHKpGBqr15PKfN3YJv

**Tags:** representation-theory, induced-representations, finite-groups, character-theory

---

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