# Basic Representation Theory, Fall 2020

HomeBasic Representation Theory, Fall 2020
## Basic Representation Theory

### Vladimir Ivanov

#### Recommended textbooks

##### Representation Theory

- W. Fulton, J. Harris, Representation theory. A first course. (Sections 1, 2, 4, 7, 8, 11, 12)
- E.B. Vinberg, Linear Representations of Groups.
- G.James, M.Liebeck, Representations and Characters of Groups. (For the first half of the course, Sections 1-20)
- B. Hall, Lie Groups, Lie Algebras, and Representations. An Elementary Introduction (For the second half of the course, Chapters 1-4)
- A. Kirillov, Jr, Introduction to Lie Groups and Lie Algebras, https://www.math.stonybrook.edu/~kirillov/mat552/liegroups.pdf (For a deeper and more general understanding of the second half of the course, Chapters 1-5)

##### Revising Linear Algebra

- S. Freidberg, A. Insel, L. Spence, Linear Algebra. (The sections without an asterisk)
- S. Axler, Linear Algebra Done Right.

##### Revising Group Theory

- C.Pinter, A book of abstract algebra. (Chapters 1-16)
- 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)

- W.Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry (Chapters 1-3)
- J.Lee, Introduction to Smooth Manifolds (for a deeper and more general picture, Chapters 1-3)
- 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)