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The Filippov n-algebra is a natural n-ary generalization of Lie algebra that is of interest in elementary particle physics. It is also of interest in combinatorics because it yields representations of the symmetric group that generalize the well studied Lie representation. Our ultimate aim is to determine the multiplicities of the irreducible representations in the representation of the symmetric group on the multilinear component of the free Filippov n-algebra with k brackets. This had been done for the ordinary Lie representation (n=2 case) by Kraskiewicz and Weyman. The k=2 case was handled in work with Friedmann, Hanlon, and Stanley. I will talk on continuing progress for general (n,k) obtained very recently with Friedman and Hanlon. Our main result shows that  the multiplicities stabilize in a certain sense when n exceeds k. As an important tool in proving this, we present two types of generalizations of Specht module involving trees.