Representation Theory (MAST90017)
Graduate courseworkPoints: 12.5On Campus (Parkville)
Overview
| Availability | Semester 2 |
|---|---|
| Fees | Look up fees |
Symmetries arise in mathematics as groups and Representation Theory is the study of groups via their actions on vector spaces. It has important applications in many fields: physics, chemistry, economics, biology and others. This subject will provide the basic tools for studying actions on vector spaces. The course will focus on teaching the basics of representation theory via favourite examples: symmetric groups, diagram algebras, matrix groups, reflection groups. In each case the irreducible characters and irreducible modules for the group (or algebra) will be analysed, developing more and more powerful tools as the course proceeds. Examples that will form the core of the material for the course include SL2, cyclic and dihedral groups, diagram algebras: Temperley-Lieb, symmetric group and Hecke algebras, Brauer and BMW algebras, compact Lie groups. Among the tools and motivation that will play a role in the study are characters and character formulas, induction, restriction and tensor products, and connections to statistical mechanics, mathematical physics and geometry.
If time permits, there may be some treatment of loop groups, affine Lie algebras and Dynkin diagrams.
Intended learning outcomes
After completing this subject students should be able to:
- understand the concepts of irreducible representations, indecomposable representations, group algebras, semisimplicity;
- understand the concepts of characters, composition series, induction and restriction;
- understand how to label representations of small groups and diagram algebras;
- describe dimensions and characters of representations of symmetric groups, dihedral groups, and cyclic groups;
- describe dimensions and characters of semisimple Lie algebras;
- give examples of nonsemisimple algebras and representations.
- have the ability to pursue further studies in this and related areas.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 4 March 2025
Eligibility and requirements
Prerequisites
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST30005 | Algebra | Semester 1 (On Campus - Parkville) |
12.5 |
Or equivalent
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 4 March 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
Up to 50 pages of written assignments (two assignments worth 25% each, due mid and late in semester)
| Second half of the teaching period | 50% |
A written examination
| During the examination period | 50% |
Last updated: 4 March 2025
Dates & times
- Semester 2
Coordinator Nora Ganter Mode of delivery On Campus (Parkville) Contact hours 36 hours comprising of 3x 1-hour lectures per week. Total time commitment 170 hours Teaching period 28 July 2025 to 26 October 2025 Last self-enrol date 8 August 2025 Census date 1 September 2025 Last date to withdraw without fail 26 September 2025 Assessment period ends 21 November 2025 Semester 2 contact information
Time commitment details
170 hours
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 4 March 2025
Further information
- Texts
- Related Handbook entries
This subject contributes to the following:
Type Name Course Ph.D.- Engineering Course Master of Science (Mathematics and Statistics) Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
Last updated: 4 March 2025