
School of Mathematics and Statistics
Jianyi Shi University of Sydney
Root systems and affine Weyl groups
Friday 20th March, 121pm, Carslaw 273.
By a root system, we mean a finite set of vertors in a euclidean space
which is stable under the reflections with respect to these vectors. In this
talk, we first consider the irreducible root systems R of the
classical types. We introduce two arrangements of positive root systems
R^{+} and discuss some properties of
R^{+}by using these arrangements.
Next we consider the affine Weyl groups W_{a} associated to
R. We
introduce two of their presentations: alcove forms and permutation forms.
We give the transition formulae between these two forms and study some
properties of W_{a} in terms of these forms.
