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A supersymmetric string model in the D=11 superspace maximally extended byantisymmetric tensor bosonic coordinates, $\Sigma^{(528|32)}$, is proposed. Itpossesses 30 $\kappa$-symmetries and 32 target space supersymmetries. The usualpreserved supersymmetry-$\kappa$-symmetry correspondence suggests that itdescribes the excitations of a BPS state preserving all but twosupersymmetries. The model can also be formulated in any $\Sigma^{({n(n+1)\over2}|n)}$ superspace, n=32 corresponding to D=11. It may also be treated as a`higher--spin generalization' of the usual Green--Schwarz superstring. Althoughthe global symmetry of the model is a generalization of the super--Poincar\'egroup, ${\Sigma}^{({n(n+1)\over 2}|n)}\times\supset Sp(n)$, it may beformulated in terms of constrained OSp(2n|1) orthosymplectic supertwistors. Wework out this supertwistor realization and its Hamiltonian dynamics.  We also give the supersymmetric p-brane generalization of the model. Inparticular, the $\Sigma^{(528|32)}$ supersymmetric membrane model describesexcitations of a 30/32 BPS state, as the $\Sigma^{(528|32)}$ supersymmetricstring does, while the supersymmetric 3-brane and 5-brane correspond,respectively, to 28/32 and 24/32 BPS states.Comment: 23 pages, RevTex4. V2: minor corrections in title and terminology,  some references and comments adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Supersymmetric string model with 30<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>κ</mml:mi></mml:math>symmetries in an extended<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>11</mml:mn><mml:mn /></mml:math>superspace and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>30</mml:mn></mml:mrow><mml:mrow><mml:mn>32</mml:mn></mml:mrow></mml:…

Supersymmetric string model with 30κsymmetries in an extendedD=11superspace and3032