Representation Theory, Math 9140b, Winter 2010
This course will study the representation theory of finite groups
and Lie groups, with a focus on the symmetric groups and linear
groups, and the relationships between these two.
Basic background in group theory, modules and linear algebra
will be assumed.
- Instructor: Dan Christensen
- E-mail: email@example.com
- Office: Middlesex 103b.
- Office Phone: 519-661-2111 x86530.
- Office Hours: after class or by appointment.
- Class times and location: Mondays and Wednesdays,
10:00 to 11:30, MC108. Starts Jan 6.
- Prerequisites: Group theory, modules and linear algebra.
Basic representation theory: irreducibility, complete reducibility,
Schur's lemma, character theory, induced representations, etc.
Representations of the symmetric groups: partitions, Young tableaux,
Young symmetrizers, Specht modules, and lots more.
Representations of the special and general linear groups:
polynomial and rational representations, complete reducibility,
characters, tensor representations, and lots more.
Text: There is no text for the course. Some
references you may like to use:
- W. Fulton, Young tableaux, LMSST 35, Cambridge Univ. Press, 1997.
- G.D. James and A. Kerber, The representation theory of the symmetric
group, Addison-Wesley or Cambridge Univ. Press, 1981. 532pp.
- Shlomo Sternberg, Group theory in physics. A pleasant book
with a conversational style and lots of applications to motivate the
- G.D. James, The representation theory of the symmetric
groups, Lecture Notes in Math., Vol. 682, 1978. 161pp.
- W. Fulton and J. Harris, Representation theory, GTM 129, Springer, 1991.
- And there are lots more!
Homework: Homework will be due roughly every two weeks.
I encourage discussion of the class material with other students, and
I encourage you to consult textbooks to learn more. But don't copy
solutions from students or texts, and when a student or a text helps
you solve a problem, you should give credit.
Presentations: In the second half of the semester,
each student will give a presentation on a topic related to the
Exam: There will be a final exam at the end of the course.
Evaluation: Evaluation will be based upon homework (40%),
presentations (30%) and the final exam (30%).
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