Timeline for What are the invariants of $U\otimes V\otimes W$ under action of $GL(U)\times GL(V) \times GL(W)$

7 events

when toggle format	what		by	license	comment
Apr 17, 2014 at 15:29	comment	added	Robert Bryant		I see that the OP has just upped the ante: Now, the case of particular interest is $(u,v,w) = (4,4,8)$ instead of $(4,4,4)$. Of course, this case will have even more invariants, though they may be harder to find. The expected dimension of the moduli space in this new case is $33$. Still, in principle, the GIT machinery will say something, though whether it will be of any use is another matter.
Apr 17, 2014 at 15:19	history	edited	Daryl Cooper	CC BY-SA 3.0	added 12 characters in body
Apr 17, 2014 at 11:20	comment	added	Robert Bryant		Are you asking for information about the ring of invariants (or covariants) (in the sense of geometric invariant theory) or for a list of normal forms with parameters? In the former case, I think that the GIT quotient (essentially, the space of orbits of the semi-stable vectors) is, in principle, understood. While I'm not sure that your particular interest ($u=v=w=4$) is worked out in the literature, the case $u=v=w=3$ is known (and the list of normal forms with parameters is known). The case $u=v=w=4$ (with $18$ moduli) is as hard as homogeneous quartics in $4$ variables, so good luck.
Apr 16, 2014 at 23:18	answer	added	Nathaniel Johnston		timeline score: 4
Apr 16, 2014 at 21:04	answer	added	Ben McKay		timeline score: 5
Apr 16, 2014 at 20:01	history	edited	Johannes Hahn	CC BY-SA 3.0	\times replaced with \otimes
Apr 16, 2014 at 19:31	history	asked	Daryl Cooper	CC BY-SA 3.0