v i i i
X-*X opposition involution on E; X = -wQ(X)
4(w) length of (a reduced expressio n of) w, for w £ W
P j standard parabolic subgroup of G containing B
and corresponding t o a subse t J Q A
L , Levi factor of P j
Lj derived group of Lj
* j root system of Lj, * j = * n ZJ
Wj Weyl group of * j , Wj i s isomorphic t o the subgroup
of W generated by SQ for a J
A
J weight lattic e for * j
(Aj)+ dominant weights of Aj
A+ "J-dominant" weights, A+ = {X e AKXa £ 0 Va e J
S(X) irreducible G-module with high weight X e A+
Sj(X) irreducible Pj-module with high weight X e A^[
MJ(M) irreducible Pj-module with low weight M £ ~A^
w, long word of Wj
L(V) vector bundle on G/H determined by V
[S(X):V] multiplicity of S(X) a s a composition factor of V
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