Oct 16 2003
Dear Professor Cvitanovic,
I have been quite intrigued by your web-book on exceptional Lie groups.
It seems that my recent paper
On tensor categories of Lie type E_N, N \not = 9, in Adv. Math. 177 (2003)
66-104
is closely related to the subject of your book. More precisely, I show
that the algebra of intertwiners on tensor powers of the minuscule
representations of Lie type E_N for N=6,7 is generated by the invariants
appearing in the second tensor power (i.e. the elements in End(V^{\otimes 2})
which commute with the group action) and one additional generator in the
(N-1)-st tensor power, for N=6,7. This is actually proved in the more general
setting of quantum groups, in which it is somewhat easier to work than in the
classical case.
Of course, I would be interested in any comments you might have, and I would
be happy to answer any questions.
Best regards,
Hans Wenzl
wenzl@math.ucsd.edu