Symmetric groups, combinatorics and characters
Block C 2010
by Jean-Baptiste Gramain (gramain(at)math.ku.dk) and Jørn Børling Olsson (olsson(at)math.ku.dk)
Please remember course evaluation in Absalon before 23. March
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.
Prerequisites:
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)