  We introduce analogs of creation and annihilation operators, related to
involutive and Hecke symmetries R, and perform bosonic and fermionic
realization of the modified Reflection Equation algebras in terms of the
so-called Quantum Doubles of Fock type. Also, we introduce Quantum Doubles of
Fock type, associated with Birman-Murakami-Wenzl symmetries coming from
orthogonal or simplectic Quantum Groups and exhibit the algebras obtained by
means of the corresponding bosonization (fermionization). Besides, we apply
this scheme to current braidings arising from Hecke symmetries R via the
Baxterization procedure.
