Basic Representation Theory, Spring 2021

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.
  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