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Representation Theory of Associative Algebras

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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

Schedule

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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