Basic Representation Theory, Fall 2023

Basic Representation Theory

Vladimir Ivanov

Syllabus of the Course

Lecture 1 notes, Lecture 1 whiteboard, Problem Set 1, Seminar 1 whiteboard

Lecture 2 notes, Lecture 2 whiteboard

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)

Revising 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).

Revising 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)

Revising 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