Brane content of branesʹ states

The problem of decomposition of unitary irreps of (super)tensorial (i.e., extended with tensorial charges) Poincaré algebra w.r.t. its different subalgebras is considered. This requires calculation of little groups for different configurations of tensor charges. Particularly, for preon states (i.e., states with maximal supersymmetry) in different dimensions the particle content is calculated, i.e., the spectrum of usual Poincaré representations in the preon representation of tensorial Poincaré. At d=4 results coincide with (and may provide another point of view on) the Vasilievʹs results in field theories in generalized space–time. The translational subgroup of little groups of massless particles and branes is shown to be (and coincide with, at d=4) a subgroup of little groups of “pure branes” algebras, i.e., tensorial Poincaré algebras without vector generators. At 11d it is shown that, contrary to lower dimensions, spinors are not homogeneous space of Lorentz group, and one have to distinguish at least 7 different kinds of preons.