## Basic Representation Theory

### Vladimir Ivanov

#### Syllabus of the Course

#### Lecture 1 notes, Lecture 1 whiteboard, Seminar 1.1 whiteboard, Seminar 1.2 whiteboard, Bonus problem 1

#### Lecture 2 notes, Lecture 2 whiteboard, Seminar 2.1 whiteboard, Seminar 2.2 whiteboard, Bonus problem 2

#### Lecture 3 notes, Lecture 3 whiteboard, Seminar 3.1 whiteboard, Seminar 3.2 whiteboard, Bonus problems 3

#### Lecture 4 notes, Lecture 4 whiteboard, Seminar 4.1 whiteboard, Seminar 4.2 whiteboard, Bonus problems 4

#### Lecture 5 notes, Lecture 5 whiteboard, Seminar 5.1 whiteboard, Seminar 5.2 whiteboard, Bonus problem 5

#### Lecture 6 notes, Lecture 6 whiteboard, Seminar 6.1 whiteboard, Seminar 6.2 whiteboard, Seminar 6.3 whiteboard, Bonus problems 6

#### Lecture 7 notes, Lecture 7 whiteboard, Seminar 7.1 whiteboard, Seminar 7.2 whiteboard, Bonus problem 7

#### Lecture 8 notes, Lecture 8 whiteboard, Seminar 8.1 whiteboard, Seminar 8.2 whiteboard, Bonus problem 8

#### Lecture 9 notes, Lecture 9 whiteboard, Seminar 9.1 whiteboard, Seminar 9.2 whiteboard, Bonus problem 9

#### Lecture 10 notes, Lecture 10 whiteboard, Seminar 10 whiteboard, Bonus problem 10

#### Lecture 11 notes, Lecture 11 whiteboard, Seminar 11 whiteboard, Bonus problem 11

#### Lecture 12 notes, Lecture 12 whiteboard, Seminar 12 whiteboard

#### 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)

##### Revising Linear Algebra.

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

##### 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)

#### Additional resources.