On the characters of the Sylow p-subgroups of untwisted Chevalley groups Y_n(p^a)

Let UY_n(q) be a Sylow p-subgroup of an untwisted Chevalley group Y_n(q) of rank n defined over F_q where q is a power of a prime p. We partition the set Irr(UY_n(q)) of irreducible characters of UY_n(q) into families indexed by antichains of positive roots of the root system of type Y_n. We focus our
attention on the families of characters of UY_n(q) which are indexed by antichains of length 1. Then for each positive root alpha we establish a one to one correspondence between the minimal degree members of the family indexed by alpha and the linear characters of a certain subquotient T_alpha of UY_n(q). For Y_n = A_n our single root character construction recovers amongst other things the elementary supercharacters of these groups. Most importantly though this paper lays the groundwork for our classification of the elements of Irr(UE_i(q)), 6 \leq i \leq 8 and Irr(UF_4(q)).