Generalized dual equivalence conjecture for Macdonald polynomials

Let $\mu$ be a partition. The operators $D_i^{\mu}$ are involutions on permutations, and a generalized dual equivalence class is an equivalence class generated by these operators. Its quasisymmetric generating function is the sum of the fundamental quasisymmetric functions associated with the inverse descent sets of its permutations.

Generalized dual equivalence conjecture. For a partition $\mu$, the quasisymmetric generating function of each generalized dual equivalence class under $D_i^{\mu}$ is symmetric and Schur positive.

This conjecture would extend the known symmetry and Schur positivity of generating functions for ordinary and twisted dual equivalence classes. The supplied text identifies it as a reformulation of an earlier conjecture but gives no resolution status.