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Organizers | Prof. Giovanni Felder, Martin Müller-Lennert |
Place | HG G 5 |
Time | Mi 15:15-17:00 |
First session | 17.9.2014 |
Contact |
Giovanni Felder Martin Müller-Lennert |
Requirements | Prerequisites: linear algebra and basic notions of algebra. Please refresh (or learn) basic notions of multilinear algebra to be able to solve the first problems on tensor products of vector spaces in [E]. |
Description | Introduction to representation theory with many examples. Lie algebras and universal enveloping algebra. Schur lemma, representations of a matrix algebra. Jordan-Holder theorem, extensions. Category O for sl(2). Representations of finite groups. Burnside theorem, Frobenius reciprocity. Representations of symmetric groups. Representations of GL_2(F_q). Quivers. McKay correspondence. |
Exercises | To each speaker, a set of exercises is assigned (see table below). The speaker is expected to solve those exercises during the semester and publish the solutions on the wiki of the seminar. |
Wiki | The password to the wiki of the seminar will be sent to the participants. |
Literature |
[E] P.Etingof et al, Introduction to representation theory, AMS, available at the Polybuchandlung http://www.polybuchhandlung.ch Much of the material (but not the historical interludes) can be found at http://math.mit.edu/~etingof/replect.pdf Additional literature that might be helpful: [F] W.Fulton, Representation theory, A first course. [L] S. Lang, Algebra. [S] J-P. Serre, Lie Algebras and Lie Groups [BGP] I N Bernstein, I M Gel'fand and V A Ponomarev "COXETER FUNCTORS AND GABRIEL'S THEOREM" Russ. Math. Surv. 28 [D] Igor Dolgachev McKay's correspondence for cocompact discrete subgroups of SU(1,1) available at http://arxiv.org/pdf/0710.2253 |
Vorlesungsverzeichnis | Vorlesungsverzeichnis |
Session | Date | Speaker | Material | Exercises | Advisor |
1 | 17.9. | Prof. Giovanni Felder | Assignment of Talks | ||
2 | 24.9. | Martin Müller-Lennert | Repetition of Tensor Products | ||
3 | 1.10. | Alessandro Lägeler | [E] 2.2 - 2.8 | [E] 6.9.3, 2.8.6 | Martin Müller-Lennert |
4 | 8.10. | Andreas Glanzer | [E] 2.9 and 2.14 - 2.16 | [E] 6.9.1 (except parts d, e), 6.9.2 | Giovanni Felder |
5 | 15.10. | Simon Willemin | [E] 3.1 - 3.6 | [E] 5.24.1, 5.24.2 | Martin Müller-Lennert |
6 | 22.10. | Louis Soares Correia | [E] 3.7 - 3.10 including exercises 3.9.1 and 3.9.5 | [E] 5.12.5, 5.16.1, 5.16.2 | Giovanni Felder |
7 | 29.10. | Tessa Turini, Guido Lob | [E] 4.1 - 4.10 and 4.12 including exercises 4.12.2 and 4.12.7 | [E] 4.12.10, 4.12.11, 5.8.4, 5.8.5, 5.11.1 | Martin Müller-Lennert |
8 | 5.11. | Angeliki Kamoutsi | [E] 5.6 - 5.11 including exercise 5.10.2 | [E] 4.12.6, 4.12.8, 4.12.9 | Giovanni Felder |
9 | 12.11. | Brunella Torricelli, Martino Stoffel | [E] 5.12 - 5.17 | [E] 3.9.2, 3.9.3, 3.9.4, 4.1.4, 4.3.1, 4.12.1 | Martin Müller-Lennert |
10 | 19.11. | Patrick Hnilicka | [E] 5.18 - 5.19 and 5.21 - 5.24 | [E] 3.8.3, 3.8.4, 3.8.5 | Martin Müller-Lennert |
11 | 26.11. | Jennifer-Jayne Jakob, Paul Steinmann | [E] 5.25, 5.27 and [F] 5.2 | [E] 2.16.2, 2.16.5, 3.6.1 | Giovanni Felder |
12 | 3.12. | Dimitrios Lekkas | [E] 6.1 including all exercises | [E] 2.11.5, 2.11.6, 2.11.7 | Giovanni Felder |
13 | 10.12. | Raul Queiroz Vale Noronha Penaguião | [E] 6.2 - 6.4 | [E] 2.7.4, 2.8.11, 2.11.3 | Martin Müller-Lennert |
14 | 17.12. | Daniel Robert-Nicoud | [E] 6.5 - 6.9 | [E] 2.3.16, 2.3.17, 2.3.18, 2.5.1 | Giovanni Felder |
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