On posets from conjugacy classes of Coxeter groups Original Research Article

Consider a conjugacy class of a Coxeter group, and define an equivalence relation on the elements using the length function. Then define a partial order on the equivalence classes, to form a partially ordered set. In this paper, we show some properties of these posets. In particular, we prove properties of the minimal elements, such as how many are there in a particular poset and how many group elements are in the minimal equivalence classes. We deal especially with the finite classical groups An, Bn, and Dn.