Math 618 Representation Theory

Spring 2021

Instructor

• jthartwig.net

Time and place

• MF 2:15pm – 3:30pm Carver 204

Text

• Lorenz, A Tour of Representation Theory

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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