Homological realization of the restricted Kostka polynomials
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2005
 arXiv:
 arXiv:math/0503058
 Bibcode:
 2005math......3058F
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory;
 17B67
 EPrint:
 23 pages