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Seminar: Representations of Lie groups - SS 17

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The representation theory of Lie groups is the fundamental tool to exploit continuous symmetries of mathematical problems. Consequently, it can be applied in virtually all areas of mathematics and is particularly useful in physics. For example,

The topic is accessed from the class of matrix Lie groups that contains many of the groups that are most relevant for applications. This approach avoids some technicalities of the general (manifold theoretic) case without oversimplifying the subject. In particular, a basic knowledge of linear algebra and analysis is sufficient for this approach.

The seminar covers some of following topics (depending on the number of participants):

Mostly, the content follows the textbook: 'Lie groups, Lie algebras, and representations' by Brian C. Hall, Springer, 2015 that can be accessed online at https://www.ub.tum.de/ebooks.

Every participant will give a one-hour presentation followed by 15-30 minutes of discussion. In addition, a summary of the content of the talk (about 5 pages) has to be written.


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Seminar   Thursday,    16:00 - 17:30,   MI 02.10.011  

Course Material

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Week 1 (27.04.2017)
Talk 1: Introduction; distribution of topics  

Week 2 (04.05.2017)
Talk 2: Matrix Lie groups Johannes Baeumler   Zusammenfassung

Week 3 (11.05.2017)
Talk 3: The matrix exponential Isabel Wagner   Zusammenfassung

Week 4 (18.05.2017)
Talk 4: Lie algebras Maximilian Hess   Zusammenfassung

Week 5 (25.05.2017)
no seminar (Christi Himmelfahrt) -  

Week 6 (01.06.2017)
Talk 6: Basic representation theory Jan Mueller   Zusammenfassung

Week 7 (08.06.2017)
Talk 7: The Baker-Campbell-Hausdorff formula Clara Bergner   Zusammenfassung

Week 8 (15.06.2017)
no seminar (Fronleichnam) -  

Week 9 (22.06.2017)
Talk 9: The Representations of sl(3;\C) Rafael Bove Barrios   Zusammenfassung

Week 10 (29.06.2017)
Talk 10: Semisimple Lie algebras Nicolas Reiter   Zusammenfassung

Week 11 (06.07.2017)
Talk 11: Root systems David Hien   Zusammenfassung

Week 12 (13.07.2017)
Talk 12: Representations of semisimple Lie algebras Dimitri Dine

Week 13 (20.07.2017)
no seminar -  

Week 14 (27.07.2017)
no seminar -  


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Representation theory
Hall   Lie groups, Lie algebras, and representations    Springer    2015       


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Organizer   Dominik Jüstel  juestelma.tum.de   MI 03.06.021   tba