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
a l OL2 0 7 _ i Oil
o —o- —o o
t*i a2 oci-2 oct-i oci
o o— —o ft *
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- —• ft
Ot\ OL2 OLi-Z Oil-2 &1-1
O- O— —O O O
6 Oct
Ei
FA
a i
*1
0
« 3 C*4
«
OC2 C
o 1
!
OL2
*3
*5
OLA

ott
~—o
OLi a2
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