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.
- The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php Select the year and scroll to the School of Physics.
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.