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 V˜1 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 V˜1 has almost polynomial growth, i.e., the sequence of codimensions of V˜1 cannot be bounded by any polynomial function but any proper subvariety of V˜1 as polynomial growth.