Abstract: Affine Kac-Moody algebras $\hat{\mathfrak{g}}$ are infinite dimensional analogs of semi-simple Lie algebras $\mathfrak{g}$ and have a central role in both Mathematics and Mathematical Physics (Conformal Field Theory).
In these lectures we will first explain how $\hat{\mathfrak{g}}$ appears naturally as a central extension of the loop algebra of a semi-simple Lie algebra $\mathfrak{g}$. Then it is possible to define a system of Chevalley generators which gives a unified point of view on $\hat{\mathfrak{g}}$ and $\mathfrak{g}$. The representation theory of $\hat{\mathfrak{g}}$ is very rich.
We study two classes of representations:
- the category O of representations: for example it contains simple
highest weight representations (they are not finite dimensional except a few ones).
- the category of finite
dimensional representations : for example it contains representations obtained by evaluation from finite dimensional
representations of $\mathfrak{g}$. $\hat{\mathfrak{g}}$ has a central element which allows to define the level of a
simple representation.
Then we will study more advanced topics as the fusion product inside the category of a given level, the critical level and applications to Knizhnik-Zamolodchikov equations.
Professor David Hernandez will be visiting CTQM from 12 to 29 October 2006.
The schedule for the Master Class is as follows:
Week 42, Auditorium D4, Bldg. 1.531, 2nd floor
Monday 16 October to Friday 20 October:
10:00-10:45 Lecture
10:45-11:15 Coffee break
11:15-12:00 Lecture
Revised 19.12.2006
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