The following is a glossary of notation which will be in effect throughout.
G will usually denote a semislmple group defined over an algebraically closed
field k of positive characteristic p.
k[G] coordinate ring of G
Rat(G) category of rational G-modules
T fixed maximal torus of G
root system of (G,T), with Dynkin diagram D
and ambient Euclidean space E
A a fixed base of •, A * {a1/...,an
B Borel subgroup of G, corresponding to A
U one dimensional root group corresponding to a
u^ fundamental dominant weight dual to a^
A weight lattice, A = Zi^,...,^}
Q root lattice, Q = ZA
A+ dominant weights, A+ = (X AKX,a £ 0 Va A)
(where X,a = 2(X,a)/(a,a) a s in [21])
W Weyl group of *, generated by reflection s Sfl, a e A
wn long word of W
v i i
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