Mathematics at Leeds University
Paul Martin's Algebra Projects Links Page
Representation theory of the symmetric group
Here we take the general machinery of ring theory and representation theory
and apply it to a specific (infinite but unified) collection of problems.
The symmetric group lies at the heart of the connection between algebra and combinatorics,
and the project also requires the student to make use of this connection.
The representation theory of the symmetric groups over the complex field is a hard problem,
but is quite well understood and treated in the research literature. It leads, however, to a
number of beautiful open problems.
Additional Notes For MSc students:
* Connection with existing MSc courses that the students will have met.
Ring theory, commutative algebra, algebraic geometry, algebras and representations
What are symmetric groups?
What is representation theory?
What in particular is the representation theory of groups?
What useful general results are there on this topic?
What specific properties of the symmetric group can be used?
How could these notions be explained to a wide audience of clever non-algebraists?
How can their "pictorial" nature be used in rigorous calculations?
- How do they connect with their applications?
(meanwhile, if you are interested, just ask me!).