Weyl Groups,Deformations of Linkage Classes,and Character Degrees For Chevalley Groups

With a Weyl group W and a positive integer p are associated p-linkage classes of weights 4,13]. Small deformations of such classes by elements of W are introduced here. These lead in turn to certain polynomials in p with highest term p^m, m = number of positive roots (one polynomial for each conjugacy class of W), which are written down explicitly for types A₁, A₂, B₂. These polynomials give (for each prime p) the degrees of the various large series of irreducible characters of the corresponding Chevalley group over the field of p elements. Indeed, the formal behavior of weights appears to reflect the actual behavior of the characters under reduction modulo p.