We study an A∞ category associated to Legendrian links in ℝ3 whose objects are n-dimensional representations of the Chekanov-Eliashberg differential graded algebra of the link. This representation category generalizes the positive augmentation category and we conjecture that it is equivalent to a category of sheaves of microlocal rank n constructed by Shende, Treumann, and Zaslow. We establish the cohomological version of this conjecture for a family of Legendrian (2,m) torus links.