Intersection of Conjugacy Classes of Chevalley Groups with Gauss Cells

Let be a proper Chevalley group or a finite twisted Chevalley group. We give some description of the intersections of noncentral conjugacy classes of with certain Gauss cells, which we call Coxeter cells. This generalizes previous results of the authors (Comm. Algebra, 1994, 22, 5935–5950; 1995, 23, 3085–3098; 1996, 24, 4447–4475). It is also the basis of yet another generalization of the same result involving weight functions on conjugacy classes.