an:02246198
Zbl 1162.17313
Feigin, Boris; Feigin, Evgeny
Homological realization of restricted Kostka polynomials
EN
Int. Math. Res. Not. 2005, No. 33, 1997-2029 (2005).
00121309
2005
j
17B67 17B55
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.