Representation Theory WS 2022/23
Schedule
Lecture:  Mondays  10:0011:30  Room 48538  Lecturer  Jun.Prof. Dr. Caroline Lassueur 
Thursdays  8:159:45  Room 48538  Lecturer  Jun.Prof. Dr. Caroline Lassueur 

Exercises:  Thursdays  11:4513:15  Room 48538  Assistant:  Marie Roth 
Office hours:  upon appointment 
Start: the 1st lecture takes place on Monday the 24th of October 2022.
Exam dates: Friday, the 14th of April.
Updates and Information
Prerequisites
Preferably, you should have already attended the lectures Character Theory and Commutative Algebra (or similar if you come from another university).
However, the necessary notions of character theory will be introduced/recalled in due course.
Exercises
The Exercises take place every week.
Exercise Sheets:
Exercise Sheets:
References and lecture notes
Literature:
The lecture is mainly based on the following textbooks:
Lecture notes:
The lecture will be based on my lecture notes from the winter semester 2020/21. However, there will be some changes, in particular a slightly different choice of topics/examples/... The notes relevant to the current week will be uploaded here every week.
Please, let me know if you find typos (of all kinds). I will correct them. Comments and suggestions are also welcome.
The lecture is mainly based on the following textbooks:
 [Web16] P. Webb, A course in finite group representation theory.
See [UniBibliothek / MathSciNet]  [EH18] K. Erdmann and T. Holm, Algebras and representation theory.
See [MathSciNet  UniBibliothek]  [LP10] K. Lux and H. Pahlings, Representations of Groups, A Computational Approach.
See [UniBibliothek / MathSciNet]  [Alp86] J. L. Alperin, Local representation theory.
See [UniBibliothek / MathSciNet]  [CR81] C. Curtis and I. Reiner, Methods of representation theory. Vol. I.
See [UniBibliothek / MathSciNet]  [Ben98] D. J. Benson, Representations and cohomology I.
See [UniBibliothek / MathSciNet]  [NT89] H. Nagao and Y. Tsushima, Representations of finite groups.
See [MathSciNet]  [Dor72] L. L. Dornhoff, Group representation theory. Part B: Modular representation theory.
See [UniBibliothek / MathSciNet]  [Nav98] G. Navarro, Characters and blocks of finite groups.
See [UniBibliothek / MathSciNet]
Lecture notes:
The lecture will be based on my lecture notes from the winter semester 2020/21. However, there will be some changes, in particular a slightly different choice of topics/examples/... The notes relevant to the current week will be uploaded here every week.
 Foreword / Conventions
 Index of notation
 Week 1:
 Week 2:
 Chapter 1: Foundations of Representation Theory, Section 5
 Chapter 2: The Structure of Semisimple Algebras, Sections 67
 Week 3:
 Chapter 2: The Structure of Semisimple Algebras, Section 8
 Chapter 3: Representation Theory of Finite Groups, Sections 912
 Week 4:
 Chapter 4: \(p\)modular systems, Sections 1314
 Chapter 5: Operations on Groups and Modules, Sections 1517 (POSTPONED to Week 5)
 Week 5:
 Chapter 5: Operations on Groups and Modules, Sections 1517
 Chapter 6: The Mackey Formula and Clifford Theory, Sections 1819
 Week 6:
 Chapter 6: The Mackey Formula and Clifford Theory, Section 20
 Chapter 7: Projective Modules, Sections 2123
 Week 7:
 Chapter 7: Projective Modules, Sections 2426
 Chapter 8: Indecomposable Modules, Section 27
 Week 8:
 Chapter 8: Indecomposable Modules, Sections 2831
 Week 10:
 Chapter 9: Lifting Results and Brauer's Reciprocity Theorem, Sections 3234
 Week 11:
 Chapter 10: Brauer Characters, Sections 3536
 Week 12:
 Chapter 11: Block Theory, Sections 3740
 Weeks 13/14:
 Chapter 12: Outlook: Further Topics, Sections 4143
(There are no lecture notes, but informal beamer/board presentations. For weight reasons, only available from Seafile via OpenOLAT)
 Chapter 12: Outlook: Further Topics, Sections 4143
Please, let me know if you find typos (of all kinds). I will correct them. Comments and suggestions are also welcome.
Oral Exam
In principle one should be able to explain the content of the lecture notes.
 Definitions, statements of the theorems/propositions/lemmata should be known.
 You should be able to explain short proofs as well as the main ideas of the longer proofs.
 You should be able to give concrete examples/counterexamples to illustrate the results.
 There can also be questions on concrete examples.
 There won't be direct questions on the Appendix.
 The Exercises mentionend in the lecture notes are important for the understanding of the theory. Their statements should be known.
 Last but not least, we expect that you are able to write down formally the concepts and results you are explaining.