KMS States on the Square of White Noise Algebra

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.