  We continue the work begun by Mickler-Moll investigating the properties of
the polynomial eigenfunctions of the Nazarov-Sklyanin quantum Lax operator. By
considering products of these eigenfunctions, we produce a novel generalization
of a formula of Kerov relating Jack Littlewood-Richardson coefficients and
residues of certain rational functions. Precisely, we derive a system of
constraints on Jack Littlewood-Richardson coefficients in terms of a simple
multiplication operation on partitions.
