The paper “On the massless modes of the AdS3/CFT2 integrable systems” has been accepted for publication in the Journal of High Energy Physics (JHEP). The 83 page paper is co-authored by Olof Ohlsson Sax (University of Utrecht), Bogdan Steganski Jr (City University London) and Alessandro Torrielli. In the paper they make a proposal for incorporating massless modes into the spin-chain of the AdS3/CFT2 integrable system. They do this by considering the alpha –> 0 limit of the alternating delta(2,1;alpha)^2 spin-chain constructed in arXiv:1106.2558. In the process they encounter integrable spin-chains with non-irreducible representations at some of their sites. They investigate their properties and construct their R-matrices in terms of Yangians. A final-form preprint of the paper can be found on the arXiv.