Riordan group concepts are combined with the basic properties of
convolution families of polynomials and Sheffer
sequences, to establish a duality law, canonical
forms

and
extensions

, where the

are polynomials in

, holding for each

in a
Riordan array. Examples

are given, in
which the

are ``orthogonal'' polynomials currently found in
mathematical physics and combinatorial analysis.
Received October 17 2008;
revised version received December 11 2008.
Published in Journal of Integer Sequences, December 11 2008.