The weyl group and the normalizer of a conditional expectation

We define a discrete group W(E) associated to a faithful normal conditional expectation E : M --> N for N subset of or equal to M von Neuman algebras. This group shows the relation between the unitary group UN and the normali zer N-E of E, which can be also considered as the isotropy of the action of the unitary group U-M of M on E. It is shown that W(E) is finite if dim Z( N) < infinity and bounded by the index in the factor case. Also sharp bound s of the order of W(E) are founded. W(E) appears as the fibre of a covering space defined on the orbit of E by the natural action of the unitary group of M. W(E) is computed in some basic examples.