Operational methods for Hermite polynomials

We exploit methods of operational nature to derive a set of new identities involving families of polynomials associated with operators providing different realizations of the Weyl group. The identities, we will deal with, extend the Nielsen formulae, valid for ordinary Hermite to families of Hermite-like polynomials. It will also be shown that the underlying formalism yields the possibility of obtaining further identities relevant to multi-variable and multi-index polynomials.