Parent BRST approach to higher spin gauge fields
The metric-like and the frame-like approaches to HS dynamics can be unified into a general framework based on the AKSZ version of the BV formalism. If the equations of motion or Lagrangian is known in e.g. metric-like form the respective unfolded equations or frame-like Lagrangian is obtained systematically using the so-called parent formulation. As an illustration I plan to consider derivation of the frame-like Lagrangian for totally symmetric HS fields starting from the Fronsdal one. In so doing one finds some intermediate formulations which turn out to be very useful for generalizations. In particular, this gives an elegant way to describe massive and (partially-)massless mixed-symmetry fields on constant curvature backgrounds. The essential ingredient of the construction on the AdS space is the so-called twisted realization of the AdS and its Howe dual symplectic algebra. By using this technique we also derive a concise form of the off-shell constraints and gauge symmetries for totally symmetric fields on AdS space at the nonlinear level, where both the local AdS and the familiar $sp(2)$-symmetry are manifestly realized.