#This is the real group of type E6, with maximal compact F4
#The Weyl group of the fundamental Cartan (which is not compact) if
#of type F4. This shows W(F4)=W(A2) semidirect W(D4)
This is the Atlas of Reductive Lie Groups Software Package version 0.2.3.
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empty: type
Lie type: E6
elements of finite order in the center of the simply connected group:
Z/3
enter kernel generators, one per line
(ad for adjoint, ? to abort):
sc
enter inner class(es): s
main: realweyl
(weak) real forms are:
0: e6(f4)
1: e6(R)
enter your choice: 0
there is a unique conjugacy class of Cartan subgroups
Name an output file (hit return for stdout):
real weyl group is W^C.((A.W_ic) x W^R), where:
W^C is isomorphic to a Weyl group of type A2
A is trivial
W_ic is a Weyl group of type D4
W^R is trivial
generators for W^C:
35
16
generators for W_ic:
34543
4
2
134565431