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