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