Entry requirements

120 credits including 90 credits mathematics. Algebraic Structures participation. Linear Algebra III participation. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, 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.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.