  We conjecture that ``Antisymmetrized Geminal Power'' wave functions, and, in
particular, those of extreme type in Coleman's terminology (i.e. with all
geminal coefficients equal), can always be rewritten as antisymmetrized
products of geminals orthogonal to each other. We prove this conjecture in
simple cases and provide numerical evidence that it holds true in more
complicated examples. Establishing the validity of this conjecture is important
as it questions the physical interpretation of AGP wavefunctions.
