Homological realization of the restricted Kostka polynomials

Details Homological realization of the restricted Kostka polynomials Homological realization of the restricted Kostka polynomials

2005-03-03

arxiv.org/abs/math/0503058v2

Mathematics

Quantum Algebra

23 pages

Scientific paper

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.

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