Basic Representation Theory, Fall 2020

Basic Representation Theory

Vladimir Ivanov

Syllabus of the Course

Lecture 1 notes, Lecture 1 whiteboard, Seminar 1.1 whiteboard, Seminar 1.2 whiteboard, Homework Assignment 1 tex, pdf file

Lecture 2 notes, Lecture 2 whiteboard, Seminar 2.1 whiteboard, Seminar 2.2 whiteboard, Homework Assignment 2 tex, pdf file

Lecture 3 notes, Lecture 3 whiteboard, Seminar 3.1 whiteboard, Seminar 3.2 whiteboard, Homework Assignment 3 tex, pdf file

Lecture 4 notes, Lecture 4 whiteboard, Seminar 4.1 whiteboard, Seminar 4.2 whiteboard, Homework Assignment 4 tex, pdf file

Lecture 5 notes, Lecture 5 whiteboard, Seminar 5.1 whiteboard, Seminar 5.2 whiteboard, Homework Assignment 5 tex, pdf file

Lecture 6 notes, Lecture 6 whiteboard, Seminar 6.1 whiteboard, Seminar 6.2 whiteboard, Homework Assignment 6 tex, pdf file

Lecture 7 notes, Lecture 7 whiteboard, Seminar 7.1 whiteboard, Seminar 7.2 whiteboard, Homework Assignment 7 tex, pdf file

Lecture 8 notes, Lecture 8 whiteboard, Seminar 8.1 whiteboard, Seminar 8.2 whiteboard, Homework Assignment 8 tex, pdf file

Lecture 9 notes, Lecture 9 whiteboard, Seminar 9.1 whiteboard, Seminar 9.2 whiteboard, Homework Assignment 9 tex, pdf file

Lecture 10 notes, Lecture 10 whiteboard, Seminar 10.1 whiteboard, Seminar 10.2 whiteboard, Homework Assignment 10 tex, pdf file

Lecture 11 notes, Lecture 11 whiteboard, Seminar 11.1 whiteboard, Seminar 11.2 whiteboard, Homework Assignment 11 tex, pdf file

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)
  5. 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
  1. S. Freidberg, A. Insel, L. Spence, Linear Algebra. (The sections without an asterisk)
  2. S. Axler, Linear Algebra Done Right.
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)