# Math 618 Representation Theory

# Spring 2021

### Instructor

### Time and place

- MF 2:15pm – 3:30pm Carver 204

### Text

### Topics

#### Representations of algebras (Part I of the book)

- multilinear algebra
- algebras, homomorphisms, modules
- irreducible and indecomposable representations, Schur's Lemma and the Krull-Schmidt Theorem
- induced and coinduced representations, adjointness relations
- primitive ideals, Jacobson radical
- semisimplicity and Wedderburn's Theorem

#### Representations of finite groups (Part II)

- Maschke's Theorem
- Frobenius reciprocity
- characters and idempotents
- Clifford theory
- symmetric group and combinatorics of Young diagrams

#### Highlights of representation theory for Lie algebras (Part III)

- universal enveloping algebra
- highest weight theory
- Weyl's character formula
- crystals

### Lecture notes

(Will be posted here.)

### Examination

Each lecture one problem is assigned.

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