← Theoretical / proof-based

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In this program

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

Advanced topics

Peter–Weyl theorem (compact groups)

Representation theory · Theoretical / proof-based

Topic

Peter–Weyl theorem (compact groups)

Practice by unit: Advanced topics

Graduate Representation Theory — scope drawn from open representation theory notes and typical US graduate representation theory syllabi.

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