Module Handbook

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Module MAT-43-26-M-7

Reflection Groups (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-43-26-M-7 Reflection Groups 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [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.
2V+1U MAT-43-26-K-7
Reflection Groups
P 42 h 93 h - - PL1 4.5 irreg.
  • About [MAT-43-26-K-7]: Title: "Reflection Groups"; Presence-Time: 42 h; Self-Study: 93 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86379 ("Reflection Groups")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Reflection groups are omnipresent in Mathematics. We concentrate on finite reflection groups over a field of characteristic zero and their
  • central examples (including symmetrical groups),
  • structural theory,
  • representation theory.

Competencies / intended learning achievements

Upon successful completion of this module, the students have become familiar with a large class of finite reflection groups over a field of characteristic zero. They learned how ubiquitous mirror groups are in Mathematics and gained deep insights into the structure and representation theory of mirror groups. They are able to name the essential statements of the lecture as well as to classify and explain the presented connections. They understand the proofs from the lecture and are able to comprehend and explain them.

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. E. Humphreys: Reflection groups and Coxeter groups,
  • G. D. James: The representation theory of the symmetric groups,
  • M. Broué: Introduction to complex reflection groups and their braid groups.

Materials

Further literature will be announced in the lecture.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

References to Module / Module Number [MAT-43-26-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.)