Representation Theory for Finite Groups
Syllabus, Master's level, 1MA056
- Code
- 1MA056
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 15 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
B.SC., Algebraic Structures and Linear Algebra III
Learning outcomes
In order to pass the course (grade 3) the student should be able to
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
Content
Groups. Linear representations of groups. Modules. Schur's lemma. Maschke's theorem. Character theory. Classification of irreducible representations. Restricted and induced representations. Frobenius's reciprocity. The Fourier transform, Fourier's inversion forumula, Plancherel's formula. Representations of the symmetric group: Young subgroups, Specht modules, Young representation. Robinson–Schensted's algorithm and bracket formula.
Instruction
Lectures and problem solving sessions.
Assessment
Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.
Reading list
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2022
- Reading list valid from Spring 2019
- Reading list valid from Autumn 2013
- Reading list valid from Autumn 2010, version 2
- Reading list valid from Autumn 2010, version 1
- Reading list valid from Spring 2010
- Reading list valid from Autumn 2008, version 2
- Reading list valid from Autumn 2008, version 1
- Reading list valid from Autumn 2007