  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.
