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REALIZATION OF THE RESTRICTED

In this paper we give two realizations of the restricted Kostka polynomials for sl2. 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 ŝl2-modules to the irreducible components. This allows to write a kind of fermionic formula for the Virasoro unitary characters.