  We argue that fermion-boson mapping techniques represent a natural tool for
studying many-body supersymmetry in fermionic systems with pairing. In
particular, using the generalized Dyson mapping of a many-level fermion
superalgebra with the SU(2) type of pairing we investigate two kinds of
supersymmetry connecting excitations in the systems with even and odd particle
numbers: dynamical supersymmetry, which ensures a unified classification of
states for both even and odd populations, and invariant supersymmetry with
actual degeneracies of states within the same supermultiplet. Dynamical
supersymmetries based on the dynamical algebra of the type U(K/2\Omega) (where
K and 2\Omega denote the number of fermion-pair and single-fermion states,
respectively) naturally arise in the bosonized description of the system.
Conditions for invariant supersymmetry are determined in a restricted case of
bilinear supercharge operators.
