Basic Representation Theory, Spring 2019

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)

  1. Problem Set 1, due February 21, pdf file, tex file
  2. Problem Set 2, due February 28, pdf file, tex file
  3. Problem Set 3, due March 7, pdf file, tex file
  4. Problem Set 4, due March 14, pdf file, tex file
  5. Problem Set 5, due March 21, pdf file, tex file
  6. Problem Set 6, due March 28, pdf file, tex file
  7. Problem Set 7, due April 11, pdf file, tex file
  8. Problem Set 8, due April 18, pdf file, tex file
  9. Problem Set 9, due April 25, pdf file, tex file