  It was shown in [AFS00] that there are only three types of irreducible
unitary representations theta of sl_2. Using the Schurmann triple one can
associate with each theta a number of representations of the square of white
noise (SWN) algebra A. However, in analogy with the Boson, Fermion and
q-deformed case, we expect that some interesting non irreducible
representations of sl_2 may result in GNS representations of KMS states
associated with some evolutions on A. In the present paper determine the
structure of the *--endomorphisms of the SWN algebra, induced by linear maps in
the 1--particle Hilbert algebra, we introduce the SWN analogue of the quasifree
evolutions and find the explicit form of the KMS states associated with some of
them.
