Theoretical / proof-based
Representation theory · Graduate · Math
Topics
Finite groups
- Definitions: representations, subrepresentations, and irreducibles
- Maschke's theorem and complete reducibility
- Characters and orthogonality relations
- Induced and restricted representations
- Burnside's theorem and applications
Lie groups and Lie algebras
- Lie groups: examples and exponential map
- Lie algebras: derivations, ideals, and semisimplicity
- Representations of sl(2, C) and weight spaces
- Root systems and Weyl group (introduction)
- Highest weight theory for semisimple Lie algebras (overview)
Advanced topics
- Peter–Weyl theorem (compact groups)
- Tensor products and Clebsch–Gordan decomposition (introduction)
- Category of representations and Schur's lemma
- Introduction to geometric representation theory
- Applications to symmetric functions and combinatorics
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$1,162 · Representation theory · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.