MAU34104 Group representations
| Module Code | MAU34104 |
|---|---|
| Module Title | Group representations |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Nicolas Mascot |
| Module Prerequisites |
MAU11100 Linear algebra and
MAU22101 Group theory |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 20% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Construct complex irreducible representations for various finite groups of small orders.
- Reproduce proofs of basic results that create theoretical background for dealing with group representations.
- Apply orthogonality relations for characters of finite groups to find multiplicities of irreducible constituents of a representation.
- Apply representation theoretic methods to simplify problems from other areas that admit symmetries.
- Identify group theoretic questions arising in representation theoretic problems, and use results in group theory to solve problems on group representations.
Module Content
- Representation of a group, examples of representations.
- Trivial representation, regular representation, equivalent representations, irreducible representations.
- Schur's lemma.
- Characters and matrix elements, orthogonality relations for matrix elements and characters.
- Representations and character table of A5.
- Representations of a product of two groups, tensor powers of a faithful representation.
- Burnside's pa qb-theorem.