Feigin, Boris; Feigin, Evgeny Homological realization of restricted Kostka polynomials. (English) Zbl 1162.17313 Int. Math. Res. Not. 2005, No. 33, 1997-2029 (2005). Summary: We give two realizations of restricted Kostka polynomials for \(\text{sl}_2\). Firstly we identify restricted Kostka polynomials with characters of the zero homology of the current algebra with coefficients in the certain modules. As a corollary we reobtain the alternating sum formula. Secondly we show that restricted Kostka polynomials are \(q\)-multiplicities of the decomposition of the certain integrable \(\widehat{\text{sl}}_2\)-modules to the irreducible components. This allows to write a kind of fermionic formula for the Virasoro unitary characters. Cited in 1 Document MSC: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B55 Homological methods in Lie (super)algebras PDF BibTeX XML Cite \textit{B. Feigin} and \textit{E. Feigin}, Int. Math. Res. Not. 2005, No. 33, 1997--2029 (2005; Zbl 1162.17313) Full Text: DOI