Seminar:
Darstellungstheorie der symmetrischen Gruppe und ihre Kombinatorik
In dem Seminar soll die
Darstellungstheorie der symmetrischen Gruppe mit ihrem
kombinatorischen und geometrischen Hintergrund behandelt werden. Der
Darstellungsring
wird mit Hilfe von Tableau und symmetrischen Funktionen beschrieben und
mit der
Geometrie von Fahnenmanigfaltigkeiten in Verbindung gebracht. Je nach
Vorkenntnissen werden Zusammenhänge mit Liealgebren und
Kac-Moody Algebren
betrachtet.
Die Literatur wird nach Interesse und Vorkenntnisse der Teilnehmer aus
der
unten angegebenen Liste ausgewählt.
Voraussetzungen: Grundkenntnisse in Algebra
Programme
The talks (more details and
references)
References
Please contact me via email if you
have any questions concerning your talk.
Here
are basic rules which you should keep in mind:
Start to prepare your talk well in
advance
The talk
should be between 60 and 90 minutes
Things you should think of during the preparation of the talk:
| What is the main result you
want to present? |
| Which definitions and small lemmas are needed
to
formulate and prove it? Which results do you want to show with complete
proof? |
| Is it maybe better to give the rough idea or
important steps
only? |
| Are there any nice examples which would help to
understand the
problem? |
|
| Come and see me or Olaf Schnuerer
latest 2 weeks before the talk
Don't hesitate to contact me if you
have any problems
|
Literaturliste:
- Sagan:
The symmetric group: Representations, Combinatorial
Algorithms and symmetric functions Springer 2001.
- Fulton:
Young tableaux, LMS Student Texts 35, 1997.
- Fulton/Harris:
Representation Theory, A first Course, Springer 1991.
- James:
The representation theory of the symmetric group, Springer LN
682, 1978.
- MacDonald:
Symmetric functions and Hall Polynomials, Oxford Science 1995.
- Kleschev:
Linear and projective representations of the symmetric group,
Cambridge 2005.
- Hong/Kang:
Introduction to Quantum groups and Crystal Bases, Graduate
Studies in Math 42, 2002
- Kac/Reina:
Bombay Lectures on Highest weight representations of infinite
dimensional Lie algebras, World Scientific 1987
- Jantzen:
Lectures on Quantum groups, Graduate Studies in Math 6,
1996.
- Grojnowski:
Affine sl(p) controls the representation theory of teh symmetric group
and related Hecke algebras. http://arxiv.org/abs/math/9907129