Let assume a Fock space written as, $$F=\bigoplus_\rho V_\rho,$$ where $V_\rho$ is an irreducible representation of $U(N)$ labeled by a partition (Young diagram) $\rho$. For the so-called bosonic case we have only single-row diagrams whereas for the fermionic case there is only single-column contributions to the expansion.
In both cases is possible to define creation-annihilation operators acting on the number-representation basis (semi-standard Young tableaux SSYT for each $\rho$) in such a way that it is possible to move one vector in this basis from one irreducible vector space to any other one in the direct sum. However, if we are working in a general expansion, where the contributions might be neither bosonic nor fermionic, it is still possible to define creation-annihilation operators? For example, to map a SSYT in representation (1) to (2,1) as we can do it from (1) to (3) or from (1) to (1,1,1) using bosonic operators or fermionic operators, respectively?