  In \cite{HRW15}, Haglund, Remmel, Wilson state a conjecture which predicts a
purely combinatorial way of obtaining the symmetric function $\Delta_{e_k}e_n$.
It is called the Delta Conjecture. It was recently proved in \cite{GHRY} that
the Delta Conjecture is true when either $q=0$ or $t=0$. In this paper we
complete a work initiated by Remmel whose initial aim was to explore the
symmetric function $\Delta_{s_\nu} e_n$ by the same methods developed in
\cite{GHRY}. Our first need here is a method for constructing a symmetric
function that may be viewed as a "combinatorial side" for the symmetric
function $\Delta_{s_\nu} e_n$ for $t=0$. Based on what was discovered in
\cite{GHRY} we conjectured such a construction mechanism. We prove here that in
the case that $\nu=(m-k,1^k)$ with $1\le m< n$ the equality of the two sides
can be established by the same methods used in \cite{GHRY}. While this work was
in progress, we learned that Rhodes and Shimozono had previously constructed
also such a "combinatorial side". Very recently, Jim Haglund was able to prove
that their conjecture follows from the results in \cite{GHRY}. We show here
that an appropriate modification of the Haglund arguments proves that the
polynomial $\Delta_{s_\nu}e_n$ as well as the Rhoades-Shimozono "combinatorial
side" have a plethystic evaluation with hook Schur function expansion.
