Leeds algebra grad course (2008/2011/2013)

Representation theory of finite dimensional algebras, with examples

This course is aimed primarily at graduate students with interests in representation theory (pure or applied), but all are welcome. The main aim is to develop techniques for studying the irreducible representations of algebras (mildly) generalising the group algebras of the symmetric groups, such as the so-called `diagram algebras'. We intend to review useful background in ring theory, matrix algebra, techniques from category theory, homological algebra, invariant theory, geometry and combinatorics. We also discuss the construction of various such interesting algebras.

Leeds Maths.

Resources

Some _very_ draft lecture notes can be made available on request. (Older versions 1 2 4 )
On representation theory of the symmetric group
References on representation theory of the symmetric group
Categories odds and ends
Algebras and Representations Leeds undergraduate module direct link (Hubery version!)
Khovanov's rep theory resources
Some random exercises

Suggested further reading

Benson, Representations and Cohomology: Basic representation theory of finite groups and associative algebras
J A Green, Polynomial representations of GLn (Springer) (version with K Erdmann and M Schocker)
Assem, Simson and Skowronski, Vol.1 (LMS ST65)
Curtis and Reiner, Representation theory of finite groups and associative algebras, Wiley Interscience
Curtis and Reiner, Methods of representation theory I, Wiley Interscience
Hamermesh, Group Theory
Gabriel and Roiter, Representations of finite-dimensional algebras
Jain and Parvathi, Noncommutative rings, group rings, diagram algebras, and their applications
...

Organiser: Paul