University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Jian-yi Shi
    University of Sydney

    Root systems and affine Weyl groups

    Friday 20th March, 12-1pm, 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 Wa 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 Wa in terms of these forms.