The Weyl group and the normalizer of a conditional expectation - Argerami, Martín (1999)
We define a discrete group W(E) associated to a faithful normal conditional expectation E : M → N for N ⊆ M von Neuman algebras. This group shows the relation between the unitary group UN and the normalizer NE of E, which can be also considered as the isotropy of the action of the unitary group UM of M on E. It is shown that W(E) is finite if dim Z(N) < ∞ and bounded by the index in the factor case. Also sharp bounds 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.