  Given any linear isometry from a Hilbert space to its square one can
explicitly construct a so-called Pythagorean unitary representation of Richard
Thompson's group F. We introduce a condition on the isometry implying that the
associated representation does not contain any induced representations by
finite-dimensional ones. This provides the first result of this kind. We
illustrate this theorem via a family of representations parametrised by the
real 3-sphere for which all of them have this property except two sub-circles.
