The Lie algebra
Last update: 24 February 2012
7 dimensional representation of
The complex simple Lie algebra of type is given by generators
The Cartan matrix is
The algebra has basis
A realization of the 7 dimensional representation of is by the matrices
Let be the corresponding Lie group of type the group generated by all the
for and Define
We use the exponentiated matrices to compute the following relations in (These relations are described in [St3].)
The first relations are commutator relations between unipotent elements.
The other needed relations describe how the Weyl group acts on the unipotent elements of
Notes and References
Where are these from?