In this program
- Finite groups
- Lie groups and Lie algebras
- Advanced topics
Advanced topics
Representation theory · Theoretical / proof-based
Peter–Weyl theorem (compact groups)
Objectives
- Peter–Weyl theorem (compact groups)
- Tensor products
- Clebsch–Gordan decomposition (introduction)
- Category of representations
- Schur's lemma
- Introduction to geometric representation theory
- Applications to symmetric functions
- Combinatorics
Study materials
- Study guideComing soon
- Exam StrategyComing soon
- Common MistakesComing soon
- WorksheetsComing soon
- Word problemsComing soon
- Mixed PracticeComing soon
- Multi-Unit ProblemsComing soon
- ReviewComing soon
- Practice testComing soon
- Answer keyComing soon
Interactive practice
Quizzes, typed answers, and flashcards for this unit — coming soon.
- Coming soon
Quiz
Multiple-choice questions with instant feedback
- Coming soon
Typed practice
Type answers and check them
- Coming soon
Flashcards
Vocabulary and key facts
- Coming soon
Mixed quiz
Harder mixed review for this standard