  In the 90's a collection of Plethystic operators were introduced in [3], [7]
and [8] to solve some Representation Theoretical problems arising from the
Theory of Macdonald polynomials. This collection was enriched in the research
that led to the results which appeared in [5], [6] and [9]. However since some
of the identities resulting from these efforts were eventually not needed, this
additional work remained unpublished. As a consequence of very recent
publications [4], [11], [19], [20], [21], a truly remarkable expansion of this
theory has taken place. However most of this work has appeared in a language
that is virtually inaccessible to practitioners of Algebraic Combinatorics.
Yet, these developments have led to a variety of new conjectures in [2] in the
Combinatorics and Symmetric function Theory of Macdonald Polynomials. The
present work results from an effort to obtain in an elementary and accessible
manner all the background necessary to construct the symmetric function side of
some of these new conjectures. It turns out that the above mentioned
unpublished results provide precisely the tools needed to carry out this
project to its completion.
