  We describe the procedure of dimensional reduction of massless fields in
$(D+1)$ dimensional Minkowski space to massive ones in $D$ dimensions in the
first-quantized setting. The procedure is compatible with Lagrangian and in a
straightforward way determines the inner product for massive fields. Howe
duality and the extensive usage of BRST formalism allows to keep the
description concise. We consider both bosonic and fermionic mixed-symmetry
fields.
