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In this paper we discuss the asymptotic spectrum of the spin chaindescription of planar N=4 SUSY Yang-Mills. The states appearing in the spectrumbelong to irreducible representations of the unbroken supersymmetry SU(2|2) xSU(2|2) with non-trivial extra central extensions. The elementary magnoncorresponds to the bifundamental representation while boundstates of Q magnonsform a certain short representation of dimension 16Q^{2}. Generalising theBeisert's analysis of the Q=1 case, we derive the exact dispersion relation forthese states by purely group theoretic means.Comment: 17 pages, No figur

The asymptotic spectrum of the Script N = 4 super-Yang-Mills spin chain