Lecture:	Mondays	10:00 - 11:30	Room 48-538	Lecturer:	Jun.-Prof. Dr. Caroline Lassueur
Exercises:	Fridays	12:00 - 13:30	Room 48-438	Instructor:	Jun.-Prof. Dr. Caroline Lassueur
Office hour:		Upon request

Link to the live stream of the FB Mathematik: http://stream.mathematik.uni-kl.de/live/
(Username/password: are the standard ones)

Public holidays / Exceptional schedule:

• 6th of June 2022: Pentecost Monday - no lecture

Office hours: you can make appointments with me for individual qusetion sessions.

Exam Dates:

Own Exam dates:
• 4th of Aug 2022 (all day, starting 8am, Registration: Frau Sternike)
• 29th of Sept 2022 (all day, starting 11am, Registration: Frau Sternike)
• 21st of Oct 2022 (all day, starting 8am, Registration: Frau Sternike)
Character Theory + Plane Algebraic Curves (with M. Schulze)

• 1st of Sept 2022 (all day, starting 8am, Registration: Frau Dietz)
• 29th of Sept 2022 (all day, starting 11am, Registration: Frau Sternike)
• 21st of Oct 2022 (all day, starting 8am, Registration: Frau Sternike)
Character Theory + Quadratic Number Fields (with C. Fieker)

• 29th of Sept 2022 (all day, starting 8am, Registration: Frau Dietz)
Character Theory + p-Adic Numbers (with G. Malle)

• upon arrangement (Registration: Frau Sternike)

• 2nd of May: The live stream of the FB Mathematik does not work at the moment. The lecture will be streamed over BBB in OpenOLAT as long as the latter does not work.
• April 2022: please register in the URM system by Friday, the 29th of April, midday.

\(LaTeX\)ed lecture notes will be uploaded here every week before the lecture.

I will essentially follow my lecture notes from the SS 2020, but ⚠ there will be changes!
Lecture Notes:

• Foreword
• Conventions
• Notation index
• Weeks 1 & 2: Chapter 1: Linear Representations of Finite Groups + Appendices A and B: Modules and Algebras (Complements) with [slides.pdf]
• Weeks 3 & 4: Chapter 2: The Group Algebra and Its Modules
• Weeks 5 & 6: Chapter 3: Characters of Finite Groups
• Week 7: no lecture, Pentcost Monday
• Weeks 8 & 9: Chapter 4: The Character Table + Appendix C: Tensor Products
  [slides X(S_4)]
• Weeks 11 & 12: Chapter 5: Integrality and Theorems of Burnside's + Appendix D: Algebraic Integers
  [slides degrees of GL_3(2)]
• Weeks 13 & 14: Chapter 6: Induction and Restriction of Characters
  [slides X(A_5)]

Full text until Week 14

The Exercise Classes take place fortnightly. They begin in the 2nd week of the lecture period and then take place every second week.

• Exercise Sheet 1. Due date: 05.05.2022, 14:00
• Exercise Sheet 2. Due date: 19.05.2022, 14:00
• Exercise Sheet 3. Due date: 02.06.2022, 14:00
• Exercise Sheet 4. Due date: 16.06.2022, 14:00 ((!) The 16th is a public holiday, if you hand in a paper version, make sure you bring it to the letter boxes before Building 48 is locked on the 15th.)
• Exercise Sheet 5. Due date: 30.06.2022, 14:00
• Exercise Sheet 6. Due date: 14.07.2022, 14:00
• Exercise Sheet 7. Due date: Wednesday 27.07.2022, 14:00 (!)

Handing in solutions: From Sheet 1 on, each fortnight, there is one exercise to hand in. (However, all exercises you would like to have corrected can be handed in!) You should hand in your solutions in handwritten form by the due date. No LaTeXed solutions accepted.
You can hand in your solutions in German/English/French/Italian.

Complete solutions to the exerices to hand in are uploaded In OpenOLAT after the corresponding deadline.

You obtain an "Übungsschein" if the following criteria are fulfilled:

• you have obtained at least 2 points out of 8 on the exercise to be handed-in in 6 Sheets out of 7;
• you have actively taken part to the exercise classes: attendance to the exercise classes + presenting at least two solutions on the board during the semester.
  

Textbooks:

• [JL01] G. James and M. Liebeck, Representations and characters of groups. See [zbMATH].
• [Ser77] J.-P. Serre, Linear representations of finite groups. See [zbMATH].
  The original text is:
  [Ser98] J.-P. Serre, Représentations linéaires des groupes finis. See [zbMATH].
• [Isa06] M. Isaacs, Character theory of finite groups. See [zbMATH].
• [Web16] P. Webb, A course in finite group representation theory. See [zbMATH].
• [CCNPW85] J.H. Conway, R.T. Curtis, S.P. Norton, R. Parker, R.A. Wilson, Atlas of Finite Groups. Clarendon Press, Oxford, 1985.

As a complement to my lecture notes, I strongly recommend Peter Webb's book, whose pre-print version is available at his webpage.

In principle one should be able to explain the content of the lecture.

• Definitions, statements of the theorems/propositions/lemmata should be known.
• You should be able to explain short proofs as well as the main arguments of the longer proofs.
• The Exercises mentioned in the lecture are important for the understanding of the theory.
• There won't be any direct questions on the content of the Appendices.
• you should also be able to give concrete examples/counter-examples to illustrate the results.
• There will also be questions on concrete examples.
• Also be ready to write down formally the concepts and results you are explaining.