Basic Representation Theory, Fall 2018

Basic Representation Theory

V. Ivanov


Syllabus of the Course


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

Homework Assignments

  1. Problem Set 1, due September 20, pdf file, tex file
  2. Problem Set 2, due September 27, pdf file, tex file
  3. Problem Set 3, due October 4, pdf file, tex file
  4. Problem Set 4, due October 11, pdf file, tex file
  5. Problem Set 5, due October 18, pdf file, tex file
  6. Problem Set 6, due November 1, pdf file, tex file
  7. Problem Set 7, due November 15, pdf file, tex file
  8. Problem Set 8, due November 22, pdf file, tex file
  9. Problem Set 9, due November 29, pdf file, tex file
  10. Problem Set 10, due December 6, pdf file, tex file