EXCEPTIONAL ALGEBRAIC GROUPS

7

map xa(t) —*

xQ(tq)

on root groups (notation of [St]). If V is a ii'X-module, we

write

V(Q)

for the iifX-module obtained from V by twisting the action of X by aq

(i.e. changing the action from v — • vx to v — • vx^).

We use Tt to denote a torus of rank i, and W(G) for the Weyl group of G. The

fundamental roots in a fundamental system for G are denoted a i , . . . , a / , and the

corresponding fundamental dominant weights are Ai,..., A/. The Dynkin diagram of

G is labelled as shown below, where the darkened nodes represent short roots.

At

Bi

Ci

Di

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