Supertwistors as quarks of SU(2,2 vertical bar 4)

The GS superstring on AdS(5) X S-5 has a nonlinearly realized, spontaneousl y broken SU(2, 2\4) symmetry. Here we introduce a two-dimensional model in which the unbroken SU(2, 2\4) symmetry is linearly realized. The basic vari ables are supertwistors, which transform in the fundamental representation of this supergroup. The quantization of this supertwistor model leads to th e complete oscillator construction of the unitary irreducible representatio ns of the centrally extended SU(2, 2\4). They include the states of d = 4 S YM theory, massless and KK states of AdS(5) supergravity, and the descendan ts on AdS(5) of the standard massive string states, which form intermediate and long massive supermultiplets. We present examples of long massive supe rmultiplets and discuss possible states of solitonic and (p, q) strings.