Figure 45: Level decomposition of the adjoint representation of into
representations of the subalgebra . The labels and indicate the simple roots
and . Level zero corresponds to the horizontal axis where we find the adjoint representation
of (red nodes) and the singlet representation (green circle about the
origin). At level one we find the two-dimensional representation (green nodes). The black
arrow denotes the negative level root and so gives rise to the level representation
. The blue arrows represent the fundamental weights and .
|