The scattering matrix for a general gl(2) spin chain

We study the general L0-regular gl(2) spin chain, i.e. a chain where the sites {i,i+L0,i+2L0,...} carry the same arbitrary representation (spin), gl(2). The basic example of such chain is obtained for L0 = 2, where we recover the alternating spin chain. Firstly, we review different known results about the integrability and the spectrum. Secondly, we give an interpretation in terms of particles and conjecture a scattering matrix connecting such chains