A Leibniz variety with almost polynomial growth

Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras image defined by the identity y1(y2y3)(y4y5)≡0. We give a complete description of the space of multilinear identities in the language of Young diagrams through the representation theory of the symmetric group. As an outcome we show that the variety image has almost polynomial growth, i.e., the sequence of codimensions of image cannot be bounded by any polynomial function but any proper subvariety of image as polynomial growth.