### Introduction to the Modular Representation Theory of Finite Groups

The following short notes provide a short recap on elementary concepts of module theory, which I will use throughout the lectures.

I assume you should have come across this material in a lecture on Rings and Modules / Commutative Algebra / Algebraic Geometry / ... If it is not the case, do not hesitate to let me know before the start of the school.

#### Lecture Notes

I have invested some time in producing a pdf version of my blackboard talks containing some general explanations and motivation about each topic treated. A first draft is available here:
You can help me improve them! Please feel free to e-mail me if you find typos or have suggestions for improvements.
If you'd like a handout of my beamer presentations as well, just drop me an e-mail.

#### Exercises

The exercises are to be found in the lecture notes. They are placed precisely where the relevant material to solve them has been presented.

#### References

Fur further reading on the topics treated in this mini-course, I recommend the following textbooks and surveys:

Notes from Summer School Lectures.
• [Bro92] M. Broué, Equivalences of blocks of group algebras. [MathSciNet]
• [Kes07] R. Kessar, Introducton to block theory. [MathSciNet]
• [Kue18] B. Külshammer, Basic local representation theory. [MathSciNet]
• [HKK10] G. Hiss, R. Kessar, B. Külshammer, An Introduction to the Representation Theory of Finite Groups [Unpublished]
• [Samb16] B. Sambale, Determination of block invariants [Unpublished]

A nice, smooth and complete introduction to representations of finite groups for beginners can be found in Peter Webb's book, which I highly recommend:
• [Web16] P. Webb, A course in finite group representation theory. [MathSciNet]

Further Books.
• [Alp86] J. L. Alperin, Local representation theory. [MathSciNet]
• [Ben98] D. J. Benson, Representations and cohomology I. [MathSciNet]
• [Cra19] D. Craven, Representation theory of finite groups: a guidebook. [MathSciNet]
• [CR81] C. Curtis and I. Reiner, Methods of representation theory. Vol. I. [MathSciNet]
• [Dor72] L. L. Dornhoff, Group representation theory. Part B: Modular representation theory. [MathSciNet]
• [EH18] K. Erdmann and T. Holm, Algebras and representation theory. [MathSciNet]
• [Lin18] M. Linckelmann, The block theory of finite group algebras. Vol. I and II.. [MathSciNet]
• [LP10] K. Lux and H. Pahlings, Representations of Groups, A Computational Approach. [MathSciNet]
• [NT89] H. Nagao and Y. Tsushima, Representations of finite groups. [MathSciNet]
• [Nav98] G. Navarro, Characters and blocks of finite groups. [MathSciNet]