Polynomial growth of the *-codimensions and young diagrams

Let A be an algebra with involution * over a field F of characteristic zero and Id(A, *) the ideal of the free algebra with involution of *-identities of A. By means of the representation theory of the hyperoctahedral group Z (2)wrS(n) we give a characterization of Id(A, *) in case the sequence of it s *-codimensions is polynomially bounded. We also exhibit an algebra G(2) w ith the following distinguished property: the sequence of *-codimensions of Id(G(2),*) is not polynomially bounded but the *-codimensions of any T-ide al U properly containing Id(G(2), *) are polynomially bounded.