Affine Springer fibers of type A and combinatorics of diagonal coinvariants
Abstract
We calculate the Borel-Moore homology of affine Springer fibers of type
A
associated to some regular semisimple nil elliptic elements. As a result, we obtain bigraded $\mf{S}_{n}$-modules whose bigraded Frobenius series are generalization of the symmetric functions introduced by Haglund, Haiman, Loehr, Remmel, and Ulyanov.