Sp(8) invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations

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We discuss twistor-like interpretation of the Sp(8) invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian Sp(8)/P which is the generalized space-time in this framework. The correspondence space C is SpH(8)/PH where SpH(8) is the semidirect product of Sp(8) with Heisenberg group SpHM and PH is some quasiparabolic subgroup of SpH(8). Spaces of functions on Sp(8)/P and SpH(8)/PH consist of QP closed functions on Sp(8) and QPH closed functions on SpH(8), where QP and QPH are canonical BRST operators of P and PH. The space of functions on the generalized twistor space T identifies with the SpH(8) Fock module. Although T cannot be realized as a homogeneous space, we find a nonstandard SpH(8) invariant BRST operator Q (Q2 = 0) that gives rise to an appropriate class of functions via the condition Qf = 0 equivalent to the unfolded higher-spin equations. The proposed construction is manifestly Sp(8) invariant, globally defined and coordinate independent. Its Minkowski analogue gives a version of twistor theory with both types of chiral spinors treated on equal footing. The extensions to the higher rank case with several Heisenberg groups and to the complex case are considered. A relation with Riemann theta functions, that are Q-closed, is discussed.