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

Abstract

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 pm, 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.