Department of Mathematics and Statistics

Dan Yasaki

MAT 701-01 (Graduate Seminar in Computational Mathematics: Representation Theory) Spring 2014

Introduction to representation theory of finite groups, Lie groups, and Lie algebras.

  • Pr. Algebra, linear algebra, basic topology
The main text for the seminar is
William Fulton and Joe Harris, Representation Theory: A First Course, Springer- Verlag, 1991.

The class meets MWF 1:00-1:50 in Petty 007.

Documents (pdf)

Homework

All questions from Fulton and Harris unless otherwise stated.
  • 1.1, 1.2, 1.10, 1.11
  • 2.2, 2.5,
    2.7: $V$ is the standard representation for $S_3$. Do this problem two ways. a. Solve the linear system arising from the character table. b. Use Corollary 2.16,
    2.21: You need to prove that the orthonormality of the rows of the character table imply $\sum_V \overline{\chi_V(g)} \chi_V(h) = \frac{|G|}{c(g)}\delta_{g,h}$, where $c(g)$ is the number of elements in the conjugacy class of $g$,
    2.22, 2.23, 2.25, 2.27
  • 3.7, 3.16, 3.23, 3.38
  • 4.4, 4.6, 4.13, 4.14