Abstract
Let F = R or C. Let V, W be two finite-dimensional vector spaces over F. Let gl(V), gl(W) be the general linear algebras of two spaces, respectively. Let X be the tensor product of V and W over F. Let f: X♁X* -> gl(V) and g: X♁X* -> gl(W) be two moment maps and let cl(O) denotes the Zariski closure of the general linear group GL(V) in gl(V). In this article, we show that for a nilpotent orbit of GL(V) in gl(V) such that O is contained in the image of f, there is a unique orbit Q such that g{f^(-1)[cl(O)]} = cl(Q).