Lecture:	Mondays	10:00-11:30	Room 48-538	Lecturer	Jun.-Prof. Dr. Caroline Lassueur
	Thursdays	8:15-9:45	Room 48-538	Lecturer	Jun.-Prof. Dr. Caroline Lassueur
Exercises:	Thursdays	11:45-13:15	Room 48-538	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 / further dates possible: get in touch with me early enough

• 24th of Oct. 22: Slides of the introduction
• Oct. 2022: Please register in the URM system so that we can contact you by e-mail; at the latest by Friday the 28th of October.

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.

The Exercises take place every week.
Exercise Sheets:

• Week 1 – Sheet 0: revision sheet on modules and algebras
• Weeks 2 and 3 - Sheet 1
• Weeks 4 and 5 - Sheet 2
• Weeks 6 and 7 - Sheet 3
• Week 8 - No exercise class
• Weeks 9 and 10 - Sheet 4
• Weeks 11 and 12 - Sheet 5
• Weeks 13 and 14 - Sheet 6

Literature:
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:
  • Appendices 1 and 2
  • Chapter 1: Foundations of Representation Theory, Sections 1-4
• Week 2:
  • Chapter 1: Foundations of Representation Theory, Section 5
  • Chapter 2: The Structure of Semisimple Algebras, Sections 6-7
• Week 3:
  • Chapter 2: The Structure of Semisimple Algebras, Section 8
  • Chapter 3: Representation Theory of Finite Groups, Sections 9-12
• Week 4:
  • Chapter 4: \(p\)-modular systems, Sections 13-14
  • Chapter 5: Operations on Groups and Modules, Sections 15-17 (POSTPONED to Week 5)
• Week 5:
  • Chapter 5: Operations on Groups and Modules, Sections 15-17
  • Chapter 6: The Mackey Formula and Clifford Theory, Sections 18-19
• Week 6:
  • Chapter 6: The Mackey Formula and Clifford Theory, Section 20
  • Chapter 7: Projective Modules, Sections 21-23
• Week 7:
  • Chapter 7: Projective Modules, Sections 24-26
  • Chapter 8: Indecomposable Modules, Section 27
• Week 8:
  • Chapter 8: Indecomposable Modules, Sections 28-31
• Week 10:
  • Chapter 9: Lifting Results and Brauer's Reciprocity Theorem, Sections 32-34
• Week 11:
  • Chapter 10: Brauer Characters, Sections 35-36
• Week 12:
  • Chapter 11: Block Theory, Sections 37-40
• Weeks 13/14:
  • Chapter 12: Outlook: Further Topics, Sections 41-43
    (There are no lecture notes, but informal beamer/board presentations. For weight reasons, only available from Seafile) [Outlook_part_I | Outlook_part_II]

Lecture Notes: Full Text WS 22/23

Please, let me know if you find typos (of all kinds). I will correct them. Comments and suggestions are also welcome.

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/counter-examples 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.