ELA, Volume 8, pp. 60-82, May 2001, abstract.
Natural group actions on tensor products of
three real vector spaces with finitely many orbits
Dragomir Z. Djokovic and Peter W. Tingley
Let G be the direct product of the general linear groups
of three real vector spaces U, V, W of finite dimensions
l, m, n (2 <= l <= m <= n). Consider the natural action
of G on the tensor product of these spaces. The number of
G-orbits in X is finite if and only if l=2 and m=2 or 3.
In these cases the G-orbits and their connected components
are classified, and the closure of each of the components
is determined. The proofs make use of recent results of
P.G. Parfenov, who solved the same problem for complex
vector spaces.