Representation Theory for Finite Groups (Contract Education)
Syllabus, Master's level, 8MA015
This course has been discontinued.
- Code
- 8MA015
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
- Finalised by
- The Faculty Board of Science and Technology, 23 April 2013
- Responsible department
- Department of Mathematics
Entry requirements
120 credit points including Algebraic Structures and Linear Algebra III, or corresponding courses
Learning outcomes
In order to pass the course (grade 3) the student should be able to
- give an account of important concepts and definitions in representation theory for finite groups;
- exemplify and interpret important concepts in specific cases;
- formulate important results and theorems covered by the course;
- describe the main features of the proofs of important theorems;
- use the theory, methods and techniques of the course to solve mathematical problems.
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
Oral examination combined with assignments given during the course.