We will discuss a class of ideals in a polynomial ring studied by Mark Haiman in his work on the Hilbert scheme of points, and ask some purely algebraic questions about them. It turns out that these questions are very closely tied to homology of affine Springer fibers, Khovanov-Rozansky homology of links, and to the ORS conjecture. We will discuss which cases are known and unknown, and compute some simple examples.