To introduce students to the modern Representation Theory by working with the classical examples: the general linear, orthogonal and symplectic groups.
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Pre-requisite knowledge for MSc students: familiarity with and maturity in algebraic structures such as groups, and in analytic structures such as metric spaces.
Occurrence | Teaching cycle |
---|---|
A | Spring Term 2022-23 |
To introduce students to the modern Representation Theory by working with the classical examples: the general linear, orthogonal and symplectic groups.
Subject content
Academic and graduate skills
Develop an appreciation of the power of combining algebraic with analytic tools learnt in the Mathematics programme, and their applicability. This course gives an essential first taste of representations to those who will go on to further study, and also an “exit level” module for those who wish to appreciate the area of Representation Theory, which is one of the major themes of modern Mathematics.
Syllabus
Task | Length | % of module mark |
---|---|---|
Closed/in-person Exam (Centrally scheduled) Representation Theory of the Classical Groups Exam |
2 hours | 60 |
Coursework - extensions not feasible/practicable Representation Theory of the Classical Groups |
N/A | 40 |
None
Task | Length | % of module mark |
---|---|---|
Closed/in-person Exam (Centrally scheduled) Representation Theory of the Classical Groups Exam |
2 hours | 60 |
Coursework - extensions not feasible/practicable Representation Theory of the Classical Groups |
N/A | 40 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
A. Barut and R. Raczka, Theory of group representations and applications, World Scientific, 1986.
W. Fulton and J. Harris, Representation theory: a first course, Springer, 1991.
R. Goodman and N. Wallach, Representations and invariants of the classical groups, CUP, 1998.
H. Weyl, The classical groups: their invariants and representations, Princeton University Press, 1997.