Affine Springer fibers of type A and combinatorics of diagonal coinvariants

We calculate the Borel-Moore homology of affine Springer fibers of type A associated with some regular semisimple nil elliptic elements. As a result, we obtain bigraded Sn-modules whose bigraded Frobenius series are a generalization of the symmetric functions introduced by Haglund, Haiman, Loehr, Remmel, and Ulyanov.