  Schur functions are the common eigenfunctions of generalized cut-and-join
operators which form a closed algebra. They can be expressed as differential
operators in time-variables and also through the eigenvalues of auxiliary
$N\times N$ matrices $X$, known as Miwa variables. Relevant for the cubic
Kontsevich model and also for spin Hurwitz theory is an alternative set of
Schur Q-functions. They appear in representation theory of the Sergeev group,
which is a substitute of the symmetric group, related to the queer Lie
superalgebras $\mathfrak{q}(N)$.. The corresponding spin $\hat{\cal
W}$-operators were recently found in terms of time-derivatives, but a
substitute of the Miwa parametrization remained unknown, which is an essential
complication for the matrix model technique and further developments. We
demonstrate that the Miwa representation, in this case, involves a fermionic
matrix $\Psi$ in addition to $X$, but its realization using supermatrices is
{\it not} quite naive.
