### Character Theory of Finite Groups SS 2017

#### Schedule

 Lecture: Tuesdays 10:00-11:30 Room 48-438 Lecturer: Jun.-Prof. Dr. Caroline Lassueur Exercises: Fridays 11:45 - 13:15 Room 48-438 Assistant: Dr. Inga Schwabrow Office hour: Mondays 13:00-14:00 Lernzentrum, odd weeks, starting 24.04.17

Exam Dates:
• 03.08.2017
• 23.08.2017
• 12.10.2017
• 13.10.2017
• 23.10.2017
Common dates with T. Hofmann are: 3.8., 23.8. und 23.10.
Please, register with Frau Sternike (Room 48-511).

#### Exercises

The exercise classes begin in the 2nd week of the lecture period and then take place every second week. See [KIS] for the precise dates.

The 1st exercise sheet will be uploaded after the 1st lecture. From Sheet 2 on, the exercise sheets will be uploaded on the handing-in day of the previous one.

Exercise Sheet 1. Due date: 26.04.2017, 14:00
Exercise Sheet 2. Due date: 10.05.2017, 14:00
Exercise Sheet 3. Due Date: 24.05.2017, 14:00
Exercise Sheet 4. Due date: 07.06.2017, 14:00
Exercise Sheet 5. Due date: 21.06.2017, 14:00
Exercise Sheet 6. Due date: 05.07.2017, 14:00
Exercise Sheet 7. Due date: 19.07.2017, 14:00

Registration: Please register for the exercises in the URM system by Friday, the 21st of April 2017, noon.

Bei Fragen zu den Übungen stehen wir Ihnen gerne zur Verfügung.

#### Übungsscheine

You obtain an "Übungsschein" if the following criteria are fulfilled:
• you have obtained minimum 50% of the points on the Exercise sheets altogether.
• you have obtained minimum 1 point in 2 Exercises (out of 4) in each of the exercise sheets 1 to 7.
• you have actively taken part to the exercise classes: attendance to the exercise classes + presenting at least one solution on the board.

Each Exercise is worth 4 points.
Exercises can be handed in in groups of maximum two students.

#### References

• [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.

#### Oral Exam

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 red lines of the longer proofs;
• the Exercises mentionend in the lecture are important for the understanding of the theory;
• you should also be able to give concrete examples/counter-examples to illustrate the results;
• there will also be questions on concrete examples.
• Please, also be ready to write down formally the concepts and results you are explaining.

#### Contents of the Lecture

• Linear representations and characters
• Character tables, orthogonality relations
• Burnside's $$p^aq^b$$-theorem
• Restriction, induction, inflation, tensor products
• Clifford theory
• Brauer's characterisation of characters

Prerequisites: elementary group theory and linear algebra