  We give a description of the image of tensor products of tautological bundles
on Hilbert schemes of points on surfaces under the Bridgeland-King-Reid-Haiman
equivalence. Using this, some new formulas for cohomological invariants of
these bundles are obtained. In particular, we give formulas for the Euler
characteristic of arbitrary tensor products on the Hilbert scheme of two points
and of triple tensor products in general.
