We study the Q-Kostka polynomials
$$L_{\lambda \mu }(t)$$
by the vertex operator realization of the Q-Hall–Littlewood functions
$$G_{\lambda }(x;t)$$
and derive new formulae for
$$L_{\lambda \mu }(t)$$
. In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials
$$Y^{\lambda }_{\mu }(t)$$
as both an analogue of the Green polynomials and deformation of the spin irreducible characters of
$$\mathfrak S_n$$
. Iterative formulas ...
