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,
 it is used to decompose partial differential equations into simpler equations on smaller spaces (the basic example is the diagonalization of linear PDOs via Fourier analysis),
 and it underlies the classification of elementary particles in physics.
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):
 basic theory of Lie groups: Lie groups, Lie algebras, exponential mapping,
 basic representation theory: unitary representations, reducibility,
 the BakerCampbellHausdorff formula,
 semisimple theory: roots, weights, Weyl groups,
 maybe compact groups.
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
onehour presentation followed by
1530 minutes of discussion. In addition, a
summary of the content of the talk (about 5 pages) has to be written.
News
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 21.03.2016: Registration for the seminar is possible from 23.01.2017 in TUMonline.
Timetable
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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 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 BakerCampbellHausdorff 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 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 
 

Literature
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People
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