TO DO LIST for my algebra grad notes (2008-)
Lecture Notes on Representation theory of finite dimensional algebras
Aimed at graduate students interested in applied representation theory.
Nominal aim is to study
representations of algebras generalising the group algebras
of symmetric groups,
such as `diagram algebras' and diagram categories.
Some _very_ draft lecture notes
(Caveats: 1. I release and modify/redact these to fit
the current lectures. 2. Draft mode means in particular that reference labels
are visible. 3. These are brief and idiosyncratic summaries - a gateway to the refs.)
This is a work in progress. Here we note some jobs that need doing
(entirely for my own organisational benefit).
Dates are gregorian-1 (cf handwritten notes etc);
numbering is from version printed 30/3/11.
- Overview/summary/quick version
- Notations/examples/statement of problem/easy stuff/bootstrapping
- General notes: categories; rings; modules; algebra reps
- Examples: S_n, T_n, P_n, B_n, Lie algebras
- 10/10/10 ss7.8 Forms...: sort it out!
- 1/8/11 ss2.5 add k-alg examples ordered by dimension
- 1/8/11 collect properties of tensor products together;
say more on R-L-handedness of modules; do right-module ver of (6.6.10)
- 1/12/11 overhaul Brauer stuff!
- 2/12/11 reorganise Cayley graph stuff - Ch.3 (geom)/8/9 (S_n).
- 12/12/12 spellcheck!
Suggested further reading
Adamek et al, Abstract and Concrete Categories
On representation theory of the symmetric group
Algebras and Representations Leeds undergraduate module
References on representation theory of the symmetric group
Khovanov's rep theory resources
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
Diestel, Graph Theory