Defining sequences for fundamental root systems and Coxeter graphs for super Weyl groups

Abstract: The purpose of this paper is double. One is to introduce defining sequences which are a kind of new descriptions of fundamental root systems for classical Lie superalgebras of type $A,B,C$ and $D$. The other one is to describe the Coxeter systems for super Weyl groups of basic classical Lie superalgebras. The super Weyl group of a basic classical Lie superalgebra is introduced and studied in [Lei Pan and Bin Shu}, which turns out to play an important role for the study of representations of the basic classical Lie superalgebra and algebraic supergroup (see [Lei Pan and Bin Shu] and [Yiyang Li and Bin Shu}). It is deserved to specially investigate super Weyl groups. These groups are proved to be some quotients of Coxeter groups. Based on defining sequences, we decide the Coxeter groups associated with those super Weyl groups via Coxeter graphs.