## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-43-12-M-7

## Module Identification

Module Number Module Name CP (Effort)
MAT-43-12-M-7 Representation Theory 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. irreg. [7] Master (Advanced) [EN] English Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Lassueur, Caroline, Jun. Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Thiel, Ulrich, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-43-12-K-7
Representation Theory
P 84 h 186 h - - PL1 9.0 irreg.
• About [MAT-43-12-K-7]: Title: "Representation Theory"; Presence-Time: 84 h; Self-Study: 186 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 86380 ("Representation Theory")

## Contents

Modules over rings and algebras:
• Theorems of Wedderburn, Jordan-Hölder and Krull-Schmidt.

Modules over group algebras:

• induction and restriction,
• the Mackey formula,
• Clifford theory,
• projective representations,
• blocks.

Representation theory of symmetric groups.

## Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand the basic propositions of group algebras and they are introduced to the essential results of the representation theory of symmetric groups. They are able to name the main propositions of the lecture, as well as to classify and explain the illustrated connections. They understand the proofs and are able to reproduce and explain them. In particular, they can critically assess what conditions are necessary for the validity of the statements.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the lecture. They have learnt how to apply the methods to new problems, analyze them and develop solution strategies independently or by team work.

## Literature

• J. L. Alperin: Local Representation theory,
• G. Navarro: Characters and blocks of finite groups,
• D. Benson: Modular Representation Theory.

## Requirements for attendance (informal)

Knowledge from the module [MAT-40-25-M-4] is useful but not necessarily required.

None

## References to Module / Module Number [MAT-43-12-M-7]

Module-Pool Name
[MAT-43-MPOOL-7] Specialisation Algebra and Number Theory (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)