On the characters of the Sylow p-subgroups of untwisted Chevalley groups Yn(pa)

Abstract

Let be a Sylow -subgroup of an untwisted Chevalley group of rank defined over where is a power of a prime . We partition the set of irreducible characters of into families indexed by antichains of positive roots of the root system of type . We focus our attention on the families of characters of which are indexed by antichains of length . Then for each positive root we establish a one-to-one correspondence between the minimal degree members of the family indexed by and the linear characters of a certain subquotient of . For our single root character construction recovers, among other things, the elementary supercharacters of these groups. Most importantly, though, this paper lays the groundwork for our classification of the elements of , , and .