Basic Representation Theory, Fall 2024

Basic Representation Theory

Vladimir Ivanov

Syllabus of the course

Linear Algebra problems, part 1, Linear Algebra problems, part 2

Lecture 1 notes, Problem Set 1

Lecture 2 notes, Problem Set 2

Lecture 3 notes, Problem Set 3

Lecture 4 notes, Problem Set 4

Lecture 5 notes, Problem Set 5

Lecture 6 notes, Problem Set 6

Lecture 7 notes

Lecture 8 notes

Lecture 9 notes

Lecture 10 notes, Problem Set 10

Lecture 11 notes, Problem Set 11

Lecture 12 notes, Problem Set 12

Lecture 13 notes, Problem Set 13

Lecture 14 notes

Recommended textbooks

Representation Theory.

1. W. Fulton, J. Harris, Representation theory. A first course. (Sections 1, 2, 4, 7, 8, 11, 12)
2. E.B. Vinberg, Linear Representations of Groups.
3. G.James, M.Liebeck, Representations and Characters of Groups. (For the first half of the course, Sections 1-20)
4. B. Hall, Lie Groups, Lie Algebras, and Representations. An Elementary Introduction (For the second half of the course, Chapters 1-4)

Reviewing Linear Algebra.

1. S. Freidberg, A. Insel, L. Spence, Linear Algebra. (The sections without an asterisk)
2. S. Axler, Linear Algebra Done Right.
3. S. Roman, Advanced Linear Algebra (Chapters 1-3, 7-11, 14, 18).

Reviewing Group Theory.

1. C.Pinter, A book of abstract algebra. (Chapters 1-16)
2. J.Fraleigh, A first course in abstract algebra. (Sections 1-14)

Reviewing Multivariable Calculus and introductory Differentiable Manifolds notions (for the second half of the course).

1. W.Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry (Chapters 1-3)
2. J.Lee, Introduction to Smooth Manifolds (for a deeper and more general picture, Chapters 1-3)
3. L.Nicolaescu, Lectures on the Geometry of Manifolds, https://www3.nd.edu/~lnicolae/Lectures.pdf (for a deeper and more general picture, Sections 1.1, 1.2, 2.1)

Additional resources.

1. Youtube channel of professor Richard E. Borcherds
2. Youtube channel of professor Steven Roman