  In this article we study the Heegaard Floer link homology of $(n, n)$-torus
links. The Alexander multigradings which support non-trivial homology form a
string of $n-1$ unit hypercubes in $\mathbb{R}^{n}$, and we compute the ranks
and gradings of the homology in nearly all Alexander gradings. We also
conjecture a complete description of the link homology and provide some support
for this conjecture. This article is taken from the author's 2007 Ph.D. thesis
and contains several open questions.
