  In this paper we give two realizations of the restricted Kostka polynomials
for $\sl_2$. Firstly we identify the restricted Kostka polynomials with a
characters of the zero homology of the current algebra with a coefficients in a
certain modules. As a corollary we reobtain the alternating sum formula.
Secondly we show that the restricted Kostka polynomials are a
$q$-multiplicities of the decomposition of the certain integrable
$\hat{\sl}_2$-modules to the irreducible components. This allows to write a
kind of fermionic formula for the Virasoro unitary models.
