Computations of Stable Multiplicities in the Cohomology of Configuration Space

We describe an algorithm to compute the stable multiplicity of a family of irreducible representations in the cohomology of ordered configuration space of the plane. Using this algorithm, we compute the stable multiplicities of all families of irreducibles given by Young diagrams with $23$ boxes or less up to cohomological degree $50$. In particular, this determines the stable cohomology in cohomological degrees $0\le i\le 11$. We prove related qualitative results and formulate some conjectures.