last modified Aug 6, 1996
Orbits of U(n,n) acting on Mn
Given x and y does there exist a linear fractional
map F so that y = F(x)? Linear fractional means
that
Also, we require the coefficient matrix and its
adjoint
to satisfy
where
As
usual we are willing to assume that all elements of our
algebra are invertible.
We wish to discover
the classical solution to the orbit problem.
It says (with lots of invertiblity conditions) that
if there is a matrix w and
an invertible matrix
w
such that
then y=F(x). Conversely, if y=F(x),
then such a w and
w
exist.
What we would like to do is use NCAlgebra
to discover this theorem. First we assume that the linear fractional
F(x) exists, and we try to produce w and
w.