Symmetric groups, combinatorics and characters  

Block C 2010

by Jean-Baptiste Gramain (gramain(at) and Jørn Børling Olsson (olsson(at)

Please remember course evaluation in Absalon before 23. March

Course information in SIS

Lectures and exercices:

Lectures: Mo 13-15 Aud 6 /We 12-14 Aud 6
Exercises: We 10-12 A102

Course material:

B. Sagan: The symmetric group [Sa]

Jørn B Olsson: Combinatorics and representations of finite groups [LN]

George Andrews, Kimmo Eriksson: Integer partitions [AE]

Jørn B Olsson: Combinatorics, Partitions and Represntation theory,  A Compendium [OC]

G James, A Kerber: The Reprsentation Theory of the Symmetric Group, Chapter 1-2  [JK]

Part of the course material: See Absalon.

Period of course:   

1. February - 15. April 2010. There will be 7 weeks of lectures and 2 weeks of project work. 

Content of course:  (Preliminary schedule)

Week 1 (JBG): Chapter 1 of Sagan's book [Sa]: Group representations (representations, characters, the symmetric group)

Week 2 (JBO): On partitions. Based on the compendium [OC] and chapters 1-3 of the book by Andrews and Eriksson [AE]

Week 3 (JBG): Parts of Chapter 2 (up to and including 2.8) of Sagan's book [Sa]: Tableaux, Specht modules for the symmetric group. The branching rule for modules. Characters of alternating groups.

Week 4 (JBO): Generating functions. Hooks in Young diagrams, beta-sets, hook structure of partitions, the hook formula,   (Chapter 1 of Olsson's book [LN] and the compendium [OC] )

Week 5-7: 
8.3 (JBG) The Murnaghan-Nakayama formula (Part of [JK])
10.3 (JBO) Cores and quotients of partitions (Chapter 3 of [LN])
15.3 (JBO) Cores of partitions, abacus-arguments (Additional material in Absalon)
17.3 (JBO) The Robinson-Schensted correspondence ([Sa] Part of Chapter 3). Column sums in character tables of symmetric groups.
(Additional material in Absalon)
22.-24.3 (JBG) (Evaluation) Blocks of characters, The Alperin-McKay conjecture etc.

Week 8-9: Projects.  List of projects available below.


Knowledge of algebra corresponding to Algebra 3

Compulsory activities:   

(1) 2 sets of written exercises in weeks 4 and 6
     First compulsory exercises pdf-file
     Second compulsory exercises pdf-file

(2) Individual work with a project including an oral presentation in April. List of Projects

Schedule for projects (New)

Informal exercise session 17. february at 11.00 pm Exercises for discussion pdf-file