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.
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