Time and Location: Mondays from 1:00 - 3:00 p.m. in SEO 612

Text: Representation Theory - A First Course by William Fulton and Joe Harris

DateSpeakerDescription (click for further details)

8/25/14Izzet CoskunCh 1 & 2: Representations of finite groups

Overview of the theory of representations of finite groups over the complex numbers, including definitions, complete reducibility, Schur's Lemma, characters and character tables, and some examples ...

9/8/14Alex StathisCh 4 & 5.1: Representations of symmetric and alternating groups

We will briefly cover group algebras, and then dive right into the theory of representations of the symmetric group S_n. In particular, we will cover Young tableaux, Young symmetrizers, the Frobenius formula, and the hook length formula, as well as prove that all the of irreducible representations of S_n come from the image of the Young symmetrizers associated to each Young diagram. We’ll follow this with a brief description of induced representations, and then the representations of the alternating group A_n. I will try to include examples where it seems helpful.

Since we will not get to the proof of the Frobenius formula, it might be worthwhile for everyone to read this carefully on their own. Exercises 4.4, 4.24, 5.2, 5.4, and 5.5 seem useful to the exposition in one way or another, so it might be prudent to do those.

9/15/14Tim RyanCh 5.2 & 6: Representations of and Schur Functors

We will begin by discussing induced representations in general by defining them and stating their properties. We then turn to the classification of representations of GL_2 (F_q), which we completely finish. Next, we will turn to definition of Schur functions in general and the statement of two results involving Schur functors and polynomials. Lastly, we will work out some examples of Schur functor problems.

Reading: Lectures: 3.3, 5.2, 6.1, 6.2, & Appendix A

Exercises: 3.15, 3.16, 3.19, 5.6, 5.7, 6.5, 6.11, 6.16, & A.30

9/22/14Janet PageCh 7 - 10: Lie Groups/Algebras, Initial Classification, Low Dimensional Examples I

9/29/14Tabes BridgesCh 7 - 10: Lie Groups/Algebras, Initial Classification, Low Dimensional Examples II

10/6/14Xudong ZhengCh 7 - 10: Lie Groups/Algebras, Initial Classification, Low Dimensional Examples III

10/13/14Chris PerezCh 11: Representations of

10/20/14Seckin AdaliCh 12 & 13: Representations of

10/27/14Gurunadh ParinandiCh 14: General Lie Algebras and the Killing form

11/3/14Sam ShidelerCh 15: Representations of

11/10/14Darko TrifunovskiCh 16 & 17: Representations of

11/17/14Seckin AdaliCh 18 & 19: Representations of

11/24/14Alex StathisCh 21: Classification of Complex Simple Lie Algebras I

12/1/14Tim RyanCh 21: Classification of Complex Simple Lie Algebras II