the main result presented in this talk is a plethystic formula for the specialization at $t = 1/q$ of the $q_{u,v}$ operators studied in [math arkiv:1405.0316]. this discovery yields elementary and direct derivations of several identities relating these operators at $t =1/q$ to the rational compositional shuffle conjecture of [math arkiv: 1404.4616]. in particular we are able to give a direct derivation of a simple formula for the symmetric polynomial $$q_{km,kn}1|_{t=1/q} \ \mbox{(for all $m,n$ co-prime and $k \geq 1 $.)}$$ we also give an elementary proof that this polynomial is schur positive. moreover, by combining our main result with the rational compositional shuffle conjecture, we obtain a completely elementary derivation of the identity expressing this polynomial in terms of parking functions in the $km \times km$ rectangle.